Social and Behavioral Statistics

Social And Behavioral Statistics

A USER-FRIENDLY APPROACH

Jeffery E. Aspelmeier Rachel Parrott

Steven P. Schacht

Instructors Manual And Test Bank SECOND Updated 2/14/06 EDITION

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Copyright 2005 by Jeffery E. Aspelmeier, Rachel Parrott, & Steven P. Schacht All rights reserved. The contents, or parts thereof, may be reproduced for use with Social & Behavioral Statistics: A user-friendly approach, by Steven P. Schacht and Jeffery E. Aspelemeier, provided such reproductions bear copyright notice, but may not be reproduced in any form for any other purposes without written permission from the copyright owner.

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Table of Contents Introduction to the Instructors Manual 4 Chapter 1: Introduction 8 Chapter 2: Basic Mathematical Concepts 11 Chapter 3: Frequency Distributions, Graphs, and Charts 14 Chapter 4: Measures of Central Tendency 20 Chapter 5: Measures of Variability 23 Chapter 6: Locating Points within a Distribution 26 Chapter 7: Probability 29 Chapter 8: Constructing Confidence 31 Chapter 9: Hypothesis Testing Between Two Sets of Observations 34 Chapter 10: Simple Regression and Correlation 39 Chapter 11: One-Way Analysis of Variance (ANOVA) 47 Chapter 12: Factorial Analysis of Variance (ANOVA) 50 Chapter 13: An Introduction to Chi-Square and Other 57

Non-Parametric Statistics

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Introduction to the Instructors Manual This manual contains the answers to all the homework problems presented in Social & Behavioral Statistics: A User-Friendly Approach by Steven P. Schacht and Jeffery E. Aspelmeier. Also, we have included additional practice exercises that could be used for the purpose of quizzes or as exam items. This introduction provides a general overview of the classroom approach that inspired this book and continues to be inspired by this book. Also, this introduction presents discussion of some issues that instructors dealing with math/statistics phobic students often face: Teaching Calculations and Homework Assignment Policies. Humor in the Classroom: Applying the User-Friendly Approach Though adding a humor based text to your curriculum is an important first step in dealing with statistics anxiety, there are a variety of ways that humor can be further integrated with the classroom experience. Though Steve touches on his use of cartoons in the classroom in the textbook introduction, I (Jeff) thought it would beneficial to present a more detailed/behavioral description of the typical classroom experience. Steve and I differed a bit on some specific practices, but our general approaches are quiet similar. As such, I will focus on Steves approach and throw in my two cents, where appropriate. Though most students are quite unaware of this, all classes start with preparation. Hours of planning typically go into each lesson, especially the first two or three times one teaches a course. A large portion of our planning goes into finding cartoons: buying the books, reading the paper (I love going to other cities and seeing the different cartoons they have), searching internet archives, looking through other textbooks, etc. You can get students involved in the toon search process by having them bring in cartoons that they think illustrate key concepts (for credit, extra-credit, or just for fun). This can be quite fruitful for you and engaging for your students; imagine a student actually thinking about statistics outside of class. Students will also bring you toons that may have little connection to course material, but they thought were funny. These cartoons can give you good ideas about what your students think is funny. Once you have amassed your stockpile of cartoons, I find it particularly useful to organize my toons based on what topics they illustrate. With some imagination, many cartoons can be used to generate data sets for a variety of statistical/parametric procedures. As I plan a class, I like to be able to choose between several cartoon options, and my selection depends on the personality of the class. In recent years, as our universitys availability of multimedia classrooms and technical support has exploded, I have expanded my humorous materials to include movie clips, sound files (a well placed Doh! from Homer Simpson can really break the tension), and web resources. This has given me many more choices and much more flexibility. Further, the continued search for more materials keeps me excited about teaching statistics. When presenting the actual lesson in class, Steve typically approached it in the following manner. He rarely if ever used canned data sets and he refused to bring a calculator to class. All example data was generated by the class, and all calculations were performed by the class. Steve

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started by giving a brief introduction to the procedure being covered that class, presented the formula, and then presented cartoon. The students then identified the variable(s) of interest and how it would be operationalized. The students then generated the data. When I do this, the format depends somewhat on the class size and the number of variables I am dealing with. For two variables with a small class, I will ask each student for two data points; one for the IV and one for the DV. For a larger class, everyone gets to pick one data point. For, classes larger than 30 (the first stats class I taught had 80 students in it). I will randomly pick a few people out of the class to generate data. Once the data is generated and recorded on the chalk board, the students are asked to perform the necessary calculations. For each step of the procedure, when you get 5 people that agree on a given answer, the answers are recorded on the board and plugged into the equations as appropriate. Steves argument for this approach was that it keeps students active, the students set the pace, and ultimately it provides the practice that students need to become proficient and feel mathematically empowered. I have found that a pleasant side effect of this approach is that you very quickly learn the students names (especially in smaller classes of 25 or fewer), educational research suggests that knowing your students names is strong predictor of positive instructor evaluations. In practice, I have found some factors that require adaptations this approach. The first factor is class size. At some critical class size, it becomes too much to have a highly interactive atmosphere. In my experience, in classes larger than 40 students begin to shut down, and almost refuse to interact. A diffusion of responsibility takes over and students are unlikely to answer questions directed to the class in general. You can ask specific students to answer, though you run the risk of embarrassing students who clearly do not know the answer, if you are not careful. Ultimately, it depends on the instructor and how comfortable you are in dealing with pregnant silence, or putting questions directly to students. I seemed to be far less comfortable with these problems than Steve, and I typically chose to adapt the approach, though not abandon it. I have found that choosing the variables of interest ahead of time, helped cut down on the awkward silence. Asking specific students to provide data points helped. Also, in these large classes, I typically brought my calculator and performed the computations with them, though I never gave my answer first. A second limiting factor is the motivation of the class. Sometimes, you get a class where none of the students are willing to perform the calculations, or more often they begin to depend on one or two students to do all the work. This can be effectively dealt with in variety of ways. For example, I have asked specific students for the answer, required a specific number of people to confirm an answer before it is accepted as correct, or in moments of great desperation I may bring my own calculator and do the calculations with them. I would note that I have rarely had a class that is this unmotivated, even when teaching statistics as 8:00 in the morning. A third limiting factor is time. As you may guess, it takes time to come up with variables, generate data, and for novice statisticians to find sums and sums of squares. Getting through one example in a 50 min class can be quite a challenge sometimes. My preference is to do two or more examples of a procedure to illustrate how it behaves under different conditions. It would be nearly impossible to achieve such goals without adapting my teaching methods. In the face of limited time, I have come to utilize spread sheets that I have pre-programmed to allow us to

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generate new data sets with unique properties and quickly arrive at the answer. I still make them do one example as a class, but for the second, third, or fourth example, I rely on the spreadsheet. I also make the spread sheet available on my web page for curious students to fiddle with later (Note: For the curious instructor, we have made some of these spreadsheets available on the instructors resource web page as well, which is accessible via http//:www.radford.edu/~jaspelme/statsbook/Social_and_Behavioral_Statistics.htm). Hand Calculations: To Round or Not to Round It is worth noting that all of the calculations conducted to generate the answers presented in this manual have been done using the arithmetic procedure outlined in Chapter 2 (p. 22 and 23). Specifically, during each step of the calculation, obtained answers are carried to the 4th decimal place without rounding. Thus, an answer of 2.345487333 would be recorded as 2.3454 and entered as such, in the next calculation. The original goal of using such procedures is to reduce the number of arithmetic/mathematical rules math phobic students would have to contend with. After more than 12 years of experience with using this method, we have found that math phobic students appreciate this convention. However, the more mathematically knowledgeable may find it rather cumbersome, and find that using more traditional rounding methods results in slightly different answers than those presented in the book. Theses differences in answers typically only affect the fourth and sometimes the third decimal place. Similarly, when the answers generated using our non-rounding method are compared with answers generated using statistical calculators and computer based statistics programs (e.g. SPSS, SAS, or Excel) slight differences may be found in the lower decimal places. In practice these differences have not been all that problematic. Students seem to handle this form of ambiguity quite well, especially when they understand the reasoning behind these discrepancies. Also, personal experience suggests that students handle this issue best, when the instructor picks one procedure (rounding or no rounding) and sticks to it. Also, allowing students to choose their preferred calculation method on an individual basis has worked well for me (never underestimate the positive effects of even a small amount of perceived control). Allowing students to decide which method they will use can make grading exams and homework a little more of a challenge for the instructor, but the headache is rather minimal. If nothing else, the whole issue does give instructors an opportunity to discuss the issue of rounding error in an applied way. Homework Assignments: Mandatory or Not With respect to course policies regarding homework assignments, new instructors often struggle with deciding how to deal with homework. Approaches to homework assignments can range between mandatory assignments graded for accuracy (a more traditional view) to making homework non-mandatory or extra credit. These approaches all have their merit and the choice of which to use depends on the type of students you expect to be teaching. With this in mind, consider the math/statistics phobic student. It may seem that having non-mandatory or extra credit only homework would be ideal for students with math and statistics anxiety. However, experience shows that students who do not practice doing the computations do not do well on exams. A happy middle ground that we have typically settled on is to make the

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homework mandatory, but grade it for completeness rather than accuracy. As long as they do all of it, even if it is wrong, they get the credit. This gives your anxiety ridden students the practice they need, and takes some of the pressure off. Also, this approach allows students to view their success on a continuum of achievement, rather than as simple categories of pass or fail. It is far more empowering to learn that you got most of a problem correct, rather than getting it all wrong. Further, it rewards students for expending effort (even if misdirected) on problems they clearly do not understand, rather than simply teaching students that you cant win so dont try. Certainly, you may find that you have some skilled students who take advantage of this policy and turn in shoddy work far below their abilities, but typically you can identify these students and let them know that you expect more. Corrections to the Instructors Manual Should you find any typos, incorrect answers, or ambiguities in this Instructors Manual, we would greatly appreciate your help in identifying these problems. You can report errors via http//:www.radford.edu/~jaspelme/statsbook/resources_for_instructors.htm . Updates will be reported in the web page and changes will be made directly to the Instructors Manual.

Conclusion As with any pedagogical tool, this is no magic bullet or a one size fits all, procrustean formula. The classroom approach that Steve and I have used works largely because we like using it. It makes teaching interesting for us and helps keep us vital as instructors. We would not do it otherwise. The purpose of the methods presented here, is not to suggest that this is how you should do it, but simply to inform and illustrate how it could be done. Happy Teaching Jeff Aspelmeier - August 2005.

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Chapter 1

Introduction

Answers to Practice Exercises 1. Parameter, Sample 2. Time, Cost, and Practicality 3. Variables 4. Personal Characteristics, Attitudes, and Behaviors 5. Humor, Math/Statistics Anxiety 6. Dependent, Independent 7. Descriptive 8. Inferential 9. Estimation Population Parameters, Tests Hypotheses Exam/Quiz Questions 1. The math associated with a population is called an/a ___________. a. statistic b. parameter c. estimate d. hypothesis 2. The math associated with a sample is called an/a ____________. a. statistic b. parameter c. estimate d. hypothesis

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3. If you counted the number of times Jerry Garcia performed Scarlet Begonias with the Grateful Dead in his lifetime by reviewing the set list for every Grateful Dead show performed, then that number would represent a ____________. However, if you estimated the number of times Jerry Garcia performed Scarlet Begonias with the Grateful Dead in his lifetime by reviewing the set lists for a single year, then that number would represent a _____________. a. statistic, parameter c. independent variable, dependent variable b. parameter, statistic d. dependent variable, independent variable 4. The professor who instructs Frank and Ernests class has often found that the length of the formula increases the number of questions asked. In this case, the length of the formula is best viewed as the _________ variable and the number of questions asked as the ___________ variable. a. independent, dependent c. invariant, constant b. dependent, independent d. constant, invariant 5. While sample statistics can be used both inferentially and descriptively, population parameters can only be used ______________. a. descriptively b. inferentially 6. All of the following are things statistics enable us to do EXCEPT: a. test hypotheses b. draw exact conclusions c. estimate population parameters d. describe the characteristics of the sample 7. For a Sample to be considered Representative of a Population, then each observation

(Individual Score) must have had an equal chance of being picked for the sample. This is known as _________________. a. Redundant Sampling c. Redundant Assignment b. Random Sampling d. Random Assignment

8. Variables that bring about a change in other variables are ___________ variables. a. Fixed c. Dependent

b. Independent d. Control 9. Variables that are expected to change as a result of variation in other variables are

____________ variables. a. Fixed c. Dependent

b. Independent d. Control 10. N =

a. Sample c. Inferential b. Population d. Non-Parametrics

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11. N-1= a. Sample c. Discrete b. Population d. Non-Parametrics

12. The study of statistics has its historical roots in all but which of the following?

a. Taxation and planning of wars in ancient Rome. b. Invention of modern computers and research databases. c. Testing of grain quality for making beer. d. Predicting shipwrecks & piracy for maritime insurance.

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Chapter 2

Basic Mathematical Concepts

Answers to Practice Exercises 1. Variables, Numerical Values, Mathematical Operations Required, and Algebraic Order. 2. a. 27 b. 41 c. 729 d. 1681 e. 81 f. 187 g. 80 h. 1680 i. 17 j. 115 k. 1107 l. 13 m. 12 n. 28 3. a. Interval-Ratio b. Nominal c. Ordinal (though it is typically treated as interval/ratio by the social sciences.) d. Interval-Ratio e. Interval-Ratio f. Nominal g. Nominal h. Nominal i. Interval-Ratio 4. a. Continuous b. Discrete c. Discrete d. Continuous e. Continuous f. Discrete g. Discrete h. Discrete i. Continuous

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Exam/Quiz Questions 1. Given the following data sets concerning a Clinton in-the-White House and usage, calculate the following (and you thought a bush in-the-White House was bad). Desire Usage (X) (Y) ------- ------- 7 6 8 7 8 7 9 8 9 8 10 10 10 11 10 12 a. X b. (X)2 c. Y2 d. (X)( Y) e. X - 1 f. (X - 1) 2. For each of the following variables, determine what level of measurement they are; nominal, ordinal, or interval-ratio. a. Desire for a Bush in-the-White House b. Usage of a Bush c. Major at School d. School Attended e. Number of Credits Taken Last Semester f. Your Ethnicity g. Final percentage in this Class h. Time spent studying for last exam 3. Now determine if these same variables are discrete or continuous. 4. Variables like attitudes and desires (usually measured on numerical rating scales) are

examples of which level of measurement? a. Nominal d. Interval/Ratio b. Ordinal

5. Variables like Major at School, Your Ethnicity, Brands of Beer, religion, or college

attended are examples of which level of measurement? a. Nominal c. Interval/Ratio b. Ordinal

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6. Variables like Your Score on this test, Number of Years of public education, Number of hours a person has listened to INSYNC, and the amount of time it takes a person to shower are examples of which level of measurement? a. Nominal c. Interval/Ratio b. Ordinal

7. Variables that are measured in non-overlapping categories, that numerically can't be

further broken down into smaller units of measure are called ________________ variables. a. Contiguous c. Discrete b. Continuous d. Discordant

8. Variables that can take on any value within a predetermined range of numbers and can be

broken down into finer units of measurement are called _________________ Variables. a. Contiguous c. Discrete b. Continuous d. Discordant

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Chapter 3

Frequency Distributions, Graphs, and Charts

Answers to Practice Exercises 1. Class Int. af cf rf crf --------------------------------------------------- 1 - 5 3 3 .25 .25 6 - 10 4 7 .3333 .5833 11 - 15 4 11 .3333 .9166 16 - 20 1 12 .0833 .9999 [1.0] a. Upper & Lower Midpoints Real Limits .5 - 5.5 3 5.5 - 10.5 8 10.5 - 15.5 13 15.5 - 20.5 18

b. Due to the limitations of the word-processing program and the formatting of the text, these graphics are not included. See main text for examples.

b3. Slice Size for pie chart Class Int. af rf Slice in Degrees -------------------------------------------------------- 1 - 5 3 .2500 .2500 x 360 = 90.0000 6 - 10 4 .3333 .3333 x 360 = 119.9880 11 - 15 4 .3333 .3333 x 360 = 119.9880 16 - 20 1 .0833 .0833 x 360 = 29.9880 Total = 359.9640 [360]

2. . Class Int. af cf rf crf --------------------------------------------------- 1 - 3 3 3 .2500 .2500 4 - 6 1 4 .0833 .3333 7 - 9 3 7 .2500 .5833 10 - 12 2 9 .1666 .7499 13 - 15 2 11 .1666 .9165 16 - 18 1 12 .0833 .9998 [1.0]

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a. Upper & Lower Midpoints Real Limits .5 - 3.5 2 3.5 - 6.5 5 6.5 - 9.5 8 9.5 - 12.5 11 12.5 - 15.5 14 15.5 - 18.5 17


b3. Slice Size for pie chart Class Int. af rf Slice in Degrees -------------------------------------------------------- 1 - 3 3 .2500 .2500 x 360 = 90.0000 4 - 6 1 .0833 .0833 x 360 = 29.9880 7 - 9 3 .2500 .2500 x 360 = 90.0000 10 - 12 2 .1666 .1666 x 360 = 59.9760

13 - 15 2 .1666 .1666 x 360 = 59.9760 16 - 18 1 .0833 .0833 x 360 = 29.9880

Total = 359.9280 [360]

3. Class Int. af cf rf crf --------------------------------------------------- 11 - 20 1 1 .0833 .0833 21 - 30 2 3 .1666 .2499 31 - 40 2 5 .1666 .4165 41 - 50 2 7 .1666 .5831 51 - 60 4 11 .3333 .9164 61 - 70 1 12 .0833 .9997 [1.0] a. Upper & Lower Midpoints Real Limits .5 - 10.5 5.5 10.5 - 20.5 15.5 20.5 - 30.5 25.5 30.5 - 40.5 35.5 40.5 - 50.5 45.5 50.5 - 60.5 55.5 60.5 - 70.5 65.5

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b3. Slice Sizes for Pie Chart Class Int. af rf Slice in Degrees

----------------------------------------------------------------- 11 - 20 1 .0833 .0833 x 360 = 29.9880 21 - 30 2 .1666 .1666 x 360 = 59.9760 31 - 40 2 .1666 .1666 x 360 = 59.9760 41 - 50 2 .1666 .1666 x 360 = 59.9760 51 - 60 4 .3333 .3333 x 360 = 119.9880 61 - 70 1 .0833 .0833 x 360 = 29.9880 Total = 359.8920 [ 360]

4. Class Int. af cf rf crf ----------------------------------------------------------------- 20 - 34 4 4 .3333 .3333 35 - 49 3 7 .2500 .5833 50 - 64 5 12 .4166 .9999 [1.0] a. LRL URL midpoint 19.5 35.5 27.5 35.5 51.5 43.5 51.5 67.5 59.5



----------------------------------------------------------------- 20 - 34 4 .3333 .3333 x 360 = 119.9880 35 - 49 3 .2500 .2500 x 360 = 90.0000 50 - 64 5 .4166 .4166 x 360 = 149.9760 Total = 359.8920 [ 360]

5. Type of Beer af cf rf crf ---------------------------------------------------------------------- Party Time Pils 1 1 .0714 .0714 Schachts Pale Ale 2 3 .1428 .2142 Marathon Malt Liq. 5 8 .3571 .5713 Duds Suds 3 11 .2142 .7855 Aspelmuts Premium Porter 3 14 .2142 .9997 [1.0]

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------------------------------------------------------------------------------------ Party Time Pilsner 1 .0714 .0714 x 360 = 26.6760 Schacht Pale Ale 2 .1428 .1428 x 360 = 51.4080 Marathon Male Liq. 5 .3571 .3571 x 360 = 128.5560 Duds Suds 3 .2142 .2142 x 360 = 77.1120 Aspelmuts Premium Porter 3 .2142 .2142 x 360 = 77.1120 Total = 360.8640 [ 360]

6. af cf rf crf midpoint --------------------------------------------------------------------------------------- 1 - 4 9 9 .2812 .2812 2.5 5 - 8 8 17 .2500 .5312 6.5 9 - 12 3 20 .0937 .6249 10.5 13 - 16 1 21 .0312 .6561 14.5 17 - 20 5 26 .1562 .8123 18.5 21 - 24 6 32 .1875 .9998 22.5 7. af cf rf crf LRL URL midpoint ------------------------------------------------------------------------------------------ 1 - 7 1 1 .04 .04 .5 7.5 4 8 - 14 2 3 .08 .12 7.5 14.5 11 15 - 21 1 4 .04 .16 14.5 21.5 18 22 - 28 4 8 .16 .32 21.5 28.5 25 29 - 35 8 16 .32 .64 28.5 35.5 32 36 - 42 9 25 .36 1.00 35.5 42.5 39

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Exam/Quiz Questions 1. The following data set concerns the number of Beavis and Butt-head episodes 18 students in your class watched this past fall. Al 3 Paula 6 Leah 4 Ed 1 Randi 15 Sue 7 Jane 7 Jeff 21 Doris 1 Anna 2 Dan 27 Mike 19 Steve 12 Josh 17 Molly 16 Paul 14 Tim 26 Ann 4 a. Using class intervals of 6, construct a frequency distribution for this data set. b. Determine the upper & lower real limits and midpoints for each interval. c. Construct a histogram and frequency polygon for this data set. 2. The first step in making a Frequency Distribution table for a set of Nominal Data (e.g. the

types of Vodka consumed on a Saturday night by dorm residents) is to create Class Intervals with which to categorize your data. a. True b. False

3. The total number of occurrences of observations for each category/class interval is called

the ___________________ Frequency. a. Cumulative c. Relative b. Absolute d. Cumulative-Relative

4. The total number of occurrences of observations for each category (or class interval)

divided by the total number of observations, is called the ______________ Frequency. a. Cumulative c. Relative b. Absolute d. Cumulative-Relative

5. A pie chart can be used to represent either quantitative or qualitative frequency data.

a. True b. False 6. E af = ?

a. 0 b. n c. 1 d. none of these

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7. Assume that a researcher wants to identify 3 specific categories of people: Those who think there are two kinds of people (we will call them 2p), people who dont think there are two kinds of people (we will call them Not 2p), those who think both of these categories are very dumb. Below are the raw number of subjects sampled who fit into each category of usage.

Category

2p Not 2p

This is just dumb

Number of Subjects by Category

15 7 20

a. Calculate the absolute frequency (af) and the relative frequency (rf) for a Qualitative Frequency Distribution (you do not need to include cumulative or cumulative-relative-frequencies). b. Use the Appropriate graphing technique to represent this data (attach on separate page if needed).

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Chapter 4

Measures of Central Tendency

Answers to Practice Exercises 1. Rank-ordered data set: 4 7 8 10 4 8 9 11 6 8 9 11 6 8 9 11 6 8 10 12 a. Mode = 8; Median = 8; Mean = 8 2. Rank-ordered data set: 7 13 19 9 14 21 10 15 22 11 16 24 12 17 26 a. Mode = (no mode); Median = 15; Mean = 15.7333 3. Rank-ordered data set: It really only makes sense to rank order the year 1952 1979 1991 1962 1983 1991 1964 1984 1991 1969 1985 1993 1978 1991 1994 a. Modes: Color = Green; Make = Honda; Year = 1991. Median = 1984 Mean = 1980.4666. 4. Unweighted Mean = 14.6666. Weighted Mean = 14.1111.

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5. Unweighted GPA = 2.8333. Weighted GPA = 3.1176 6. a. mode = 10.5 & 14.5 median = 13.1250 mean = 15.8333 b. The results from grouped data are less accurate. 7. a. severely positively (right) skewed b. symmetrical (slightly negatively skewed) c. positively (right) skewed d. negatively (left) skewed e. negatively (left) skewed (the Median score is a type, it should be 115, not 15) f. symmetrical

g. distribution a is probably the most strongly skewed if we assume that the lower limit of the scale is 1 or 0. The other examples probably have a larger range of scores so the relative distance between the mean, median, and mode are smaller.

Exam/Quiz Questions 1. The following represents scores on a recent 10 point quiz that Calvin and his classmates took. 1 -- Calvin? 5 7 9 6 9 10 7 10 8 7 7 7 8 6 a. Calculate the mode, median, and mean for this data set. 2. Assuming that Calvin would ever attend college, lets say that the following represents his grades for the past two semesters. (Note: A = 4, B = 3, C = 2, D = 1, F = 0) Basic Basket Weaving C (3 credits) Golf B (2 credits) Juvenile Delinquency A (5 credits) Deviance A (5 credits) Biology C (2 credits) Sociology C (2 credits) Math D (3 credits) Statistics C (3 credits) a. Calculated his unweighted and weighted G.P.A.s.

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b. Which would you rather have? 3. Which of the following measures directly considers every value in a data set in its calculation? A. Median C. Mean B. Mode D. All of the above 4. Which of the following is a single value that lets us summarize a whole data set?

a. Frequency Distribution c. Outlier b. Measure of Central Tendency d. All of the Above 5. It is possible for a data set to have no mode. a. True b. False 6. It is possible for a data set to have many modes. a. True b. False 7. It is possible for a data set to have multiple medians. a. True b. False 8. An instructor had students rate their statistics anxiety on a scale of 1 to 7. The class mean was 5.5, the median was 3, and the mode was 2. Which of the following best describes this distribution of data? a. Positively (right) Skewed c. Negatively (left) Skewed b. Symmetrical d. It has multiple modes 9. (This problem could be paired with Exam/quiz question 7 from the previous chapter). Assume that a researcher has identified 3 specific categories of people: Those who think there are two kinds of people (we will call them 2p), people who dont think there are two kinds of people (we will call them Not 2p), those who think both of these categories are very dumb. The researcher also collected information on the average number of times per week group members categorized other people. The group frequencies and averages are presented below. Calculate the Weighted Mean. Average Number of times per Week Category Absolute Frequency Group Members Categorize People 2p 15 20.5 Not 2p 7 5.1 This is very dumb 20 4.2

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Chapter 5

Measures of Variability

Answers to Practice Exercises 1. a. 13 b. Sample Variance = 14.3657 Sample S. D. = 3.7902 c. Population Variance = 13.6475 Population S. D. = 3.6942

d. Population variance; the variance is squared. (Note: There is a mistake in the question. The question should ask students to compare the Sample Variance and Population Variance or the Sample Standard Deviation and Population Standard Deviation. The answer would be that the sample variance or sample standard deviation are both larger than their respective population values, because the denominator for the sample statistics is smaller (n-1 vs. N) and result in a larger quotient.)

2. a. 26 b. Population Variance = 47.1616 Population S. D. = 6.8674 c. Sample Variance = 49.1266 Sample S. D. = 7.009.

d. Thirteen year olds question parental authority more often than 6 year olds. Moreover, they also have a wider range in their scores and larger variance and standard deviation scores. That is, there is more variability in the number of times 13 year olds question authority, compared to six year-olds.

3. a. 11 b. Sample Variance = 13.9238 Sample S. D. = 3.7314 c. Population Variance = 12.9955 Population S. D. = 3.6049 4. a. s2 = 29.5238 s = 5.4335 b. s2 = 142.0952 s = 11.9203

c. There is greater variability in the number of penguins seen by English students, compared to the number of penguins seen by statistics students.

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Exam/Quiz Questions 1. The following data set represents the number of hours spent crawling on the desert floor before a person begins to hallucinate. 4 8 18 3 7 3 16 15 n = 16 4 15 8 8 10 2 12 13 a. Calculate the range. b. Using the appropriate formulas, calculate the variance and standard deviation scores. 2. Measures that tell us how our data is dispersed within a data set are known as measures of _______________.

a. Centrality b. Variability c. Probability 3. A ______________ is a simple measure of the distance between the largest and smallest observations in a data set.

a. Variance b. Standard Deviation c. Range d. Z-score 4. The Standard Deviation and Variance will always be larger when measuring data from a _____________. a. Single Subject b. Population c. Sample d. None of the above

5. Assume that a scientist measured the number of grilled-cheese-sandwiches that concert-goers bought in the parking-lot after a Grateful Dead show, and he found that on the first night the 10 people he randomly sampled all bought 5 grilled-cheese-sandwiches. On the second night, he found of the 10 people sampled, 2 people bought 3 sandwiches, 2 people bought 4 sandwiches, 2 people bought 5 sandwiches, 2 people bought 6 sandwiches, and 2 people bought 7 sandwiches. Which of the following is true:

a. There was more variance in the number of sandwiches bought on the first night. b. There was more variance in the number of sandwiches bought on the second night. c. There was no difference in variance for either night. d. There were more sandwiches bought the second night than on the first. 6. Which of the following measures does NOT consider every element in a data set for its calculation? a. Range b. Variance c. Standard Deviation d. None of these 7. For data that is normally distributed (symmetrical), 3(X-0) = ? A. 1 B. 0 C. -1 8. A measure of variance or standard deviation (e.g. s2 or s) can never be negative. A. True B. False

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C. Assume that a scientist is interested in measuring the number of thoughts per minute the average nine year old has when watching Television as compared to when they read a Book. The scientist measured two groups of nine-year-olds with 8 members in each group. One group was measured while watching Television and the other while reading a Book. The data is given below. # of Thoughts per min # of Thoughts per min Subject TV Group Subject Book Group 1 3 1 1 2 4 2 2 3 5 3 3 4 6 4 6 5 6 5 6 6 7 6 9 7 8 7 10 8 9 8 11 a. Find the Mean, Median, and Mode for each data set. b. Find the s2 for both data sets. c. Find the s for both data sets. d. Looking at the means and standard deviations of the TV and Book data sets, what conclusions can you draw about the number of thoughts these two forms of entertainment inspire.

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Chapter 6

Locating Points Within a Distribution

Answers to Practice Exercises 1. a. 15th b. 25th c. 75th d. 50th e. 45th 2. a. .1587 (15.87%) b. .5000 (50.00%) c. .3747 (37.47%) d. .0228 (02.28%) e. .2546 (25.46%) f. .1628 (16.28%) 3. a. 119.20 IQ b. 94.15 IQ c. 100.00 IQ d. 84.40 IQ e. 109.15 IQ 4. a. .0485 (04.85%) b. .0062 (00.62%) c. .0994 (09.94%) d. .7967 (79.67%) e. .0062 (00.62%) f. .1548 (15.48%) 5. a. 65.6080 Inches b. 66.5920 Inches c. 62.1520 Inches d. 63.2080 Inches e. 64.0000 Inches 6. a. 22.66th b. 93.32nd c. 06.68th d. 99.87th

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7. a. 10.56th b. 50.00th c. 26.76th d. 89.44th e. 85.08th f. 98.08th Exam/Quiz Questions 1. Given the following information on IQs for students who believe that ignorance is not bliss and who do not drive their wagons over cliffs, = 110 IQ = 20 IQ What is the probability that the next such person you will meet will have an IQ: a. 110 or less? b. 130 or greater? c. 105 or greater? d. 95 or less? e. between 102 and 115? f. between 95 and 100? g. between 117 and 125? h. between 110 and 114? 2. Using this same information, what IQ score is, a. 85% of the population equal to or less than? b. 25% of the population equal to or less than? c. 50% of the population equal to or less than? d. 15% of the population equal to or less than? 3. A ______________ is a measure that tells us the number of standard deviations an individual score is

from the mean. A. Z-score D. Both B and C B. Z of X E. Both A and B C. Q-score 4. A _______________ is a measure that tells us where a given observation is located in a data set,

in terms of its probability of occurrence, relative to the whole distribution. A. Variance C. Z-score B. Mean Deviation D. Standard Deviation

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5. A _____________ is a measure that designates where your score is located relative to the percentage of people who scored below your score.

A. Percentile Rank C. Mean Deviation B. Variance D. Z-score 6. If you were interested in knowing the Z-score associated with having a Percentile Ranking of 89,

then you would find the corresponding Probability Value of .8900 in which column of Appendix 1?

A. Column 2, "The Area from mean to z" B. Column 4, "The Small Part" C. Column 5, "The Big Part" 7. The normal curve is also known as _____________.

A. A Z-Score Distribution C. A Gaussian Distribution B. A Bell-Shaped Curve D. All of the above

29

Chapter 7

Probability

Answers to Practice Exercises 1. a. .5000 (50.00%) b. .1250 (12.50%) c. .0961 (09.61%) d. .2692 (26.92%) e. .0312 (03.12%) f. .0833 (08.33%) 2. a. .0833 (08.33%) b. .0047 (00.47%) c. .0090 (00.90%) 3. a. .1640 (16.40%) b. .0175 (01.75%) c. .0729 (07.29%) d. .7329 (73.29%) Exam/Quiz Questions 1. Assuming that they would even want another child, especially considering the one they already have, what is the probability of Calvins parents having another boy? 2. Using a randomly shuffled deck of 52 cards, what is the probability of drawing a red Queen or a Jack? 3. Using a randomly shuffled deck of 52 cards, what is the probability of drawing an Ace, or a six, or a ten? 4. What is the probability of having four female children (births) in a row? 5. What is the probability of randomly selecting the top three finishers of a race, in the exact order of them finishing, out of a race comprised of six total racers? 6. What is the probability of getting three heads out of seven consecutive flips of a coin? 7. What is the probability of having three or fewer female children out of six consecutive births?

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8. A graph of the probability of occurrence for all possible outcomes in a given set of instances (i.e. the number of heads tossed out of 8 consecutive coin flips) shares which of the following properties with a Z-score distribution:

A. It is Symmetrical in Shape. B. Probability Values are lowest at the tails. C. Probability Values are greatest at the center. D. Assumes a Bell-Shaped Distribution E. All of the above. 9. 0! = ?

A. 0 B. 1 C. neither a or b 10. Probability Operations that are concerned with outcomes that occur in a certain order and

assume that replacement is not occurring are called _____________________. A. Permutations C. Factorials

B. Combinations D. Preambulations

31

Chapter 8

Constructing Confidence Intervals

Answers to Practice Exercises 1. a. 9 b. 1.764 c. 20.236 < < 23.764, .05 2. a. 3 b. 7.74 c. 392.26 < < 407.74, .01 3. a. 2 b. 4.084 (.05, t crit. for df of 35 = 2.042); 5.5 (.01, t crit. for df of 35 = 2.750). c. 38.916 < < 47.084, .05 37.5 < < 48.5, .01 d. As we become more confident in the interval estimate, its width increases. 4. a. 10.9544, 1.0954, 2.1688 (.05, t crit. for df of 119 = 1.98) 40.8312 < < 45.1688, .05

b. As we increase our sample size, the sample is more likely to be representative of the population. Therefore we are can have greater confidence that our sample mean reflects the population mean with smaller interval estimates (i.e. the width decreases)

5. a. 701; 1214 b. 11,203; 19,411

c. Without question, a margin of error of 2 pounds is far more economically feasible.

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Exam/Quiz Questions 1. Using Cartoon 8.1 as a backdrop, lets say we are interested in the average number of personals placed in newspapers throughout the U.S. We find the following: Mean (x-bar) = 35 Ads Population S.D. = () = 10 N = 25 a. Calculate the standard error of the mean. b. With the confidence level set at 99%, construct the confidence limit. c. Using this confidence limit, construct a confidence interval for this data. 2. Lets say we are now interested in the number of sexist personals placed in newspapers throughout the U.S. We find the following: Mean (x-bar) = 21 Ads Sample S.D. (s) = 12 n = 9 a. Calculate the standard error of the mean. b. With the confidence level set at 99.9%, construct the confidence limit. c. Using the confidence limit, construct a confidence interval for this data. 3. Using the previously used information on IQs, = 100 = 15 a. How large of a sample would we need to estimate the mean with a margin of error of 10 IQ points (alpha = .01)? b. How large of a sample would we need to estimate the mean with a margin of error of 5 IQ points (alpha = .05)? 4. Confidence Intervals are examples of which of the following? A. Inferential Parameters C. Descriptive Statistics B. Descriptive Parameters D. Inferential Statistics 5. Which of the following is not true of the t-distribution? A. As sample size approaches 120, it approximates a normal distribution. B. It was developed at a brewing company in Ireland to test the quality of ingredients. C. The t-distribution is flatter and less peaked than the z-distribution. D. A t-distribution is a probability distribution for standardized scores obtained from a sample. E. All of the above. 6. In terms of the Standard Error of the Mean, increasing the size of a sample does what to the width

of a confidence interval. A. Decrease Standard Error of the Mean and Decrease the width of the Confidence Interval. B. Increase the Standard Error of the Mean and Decrease the width of the Confidence Interval. C. Decrease the Standard Error of the Mean and Increase the width of the Confidence Interval. D. Increase the Standard Error of the Mean and Increase the width of the Confidence Interval.

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7. The Degree to which a sample statistic potentially deviates from the parameter it is estimating is

called _______________. (e.g. the value you would need to + to the sample mean) A. Margin of Error C. Confidence Limits B. Sample Error D. All of the above 8. In terms of a Confidence Interval, which of the following Confidence Levels will give you the

largest error level (). A. 90% D. 95% B. 99.9% E. None of these, error level and confidence level are unrelated. C. 99% 9. If you are calculating Confidence Intervals from a sample where you know (s) and not (), then

what effect would increasing the sample size have the value of (t/2) and the resulting width of the Confidence Interval.

A. Increase t-value and increase the width of the Confidence Interval. B. Increase t-value and decrease the width of the Confidence Interval. C. Decrease t-value and decrease the width of the Confidence Interval. D. Decrease t-value and increase the width of the Confidence Interval. 10. Increasing the Sample Size and Increasing the Confidence Level (i.e. 95% to 99%) are both ways

to limit the possibility that the true population mean will fall outside the ends of the Confidence Interval, but increasing which one will give you the most accurate and narrow Confidence Interval?

A. Increasing Sample Size B. Increasing Confidence Level 11. If you have a Confidence Interval of (24.9 < < 35.1), .001, calculated using (s) and not (),

Then you would conclude which of the following?

A. 99 times our of 100 the population mean will fall between 24.9 and 35.1 and 1 time out of 100 the pop. mean will fall outside of these values. B. 1 time out of 100 the population mean will fall between 24.9 and 35.1 and 99 times out of 100 it will fall outside of these values. C. 1 time out of 1000 the population mean will fall between 24.9 and 35.1 and 999 times out of 1000 it will fall outside of these values. D. 999 times out of 1000 the population mean will fall between 24.9 and 35.1 and 1 time out of 1000 it will fall outside of these values.

34

Chapter 9

Hypothesis Testing Between Two Sets of Observations

Answers to Practice Exercises 1. a. The appropriate test is a Z test, since we know the sample mean, population mean, and

the population Standard Deviation. |6| Z obtained > 1.96 Z critical; thus, the average number of times Brown Swiss cows touch the electric fence significantly differs from the national average. That is, Brown Swiss cows touch the fence more often than the average cow, and this may indicate that Brown Swiss cows may be less intelligent that other cows.

b. Reject the null hypothesis and fail to reject the research/alternative hypothesis. 2. a. The appropriate test is a Z test, since we know the sample mean, population mean, and

the population Standard Deviation |1.6666| Z obtained < 1.96 Z critical; thus, the average number to times Guernsey cows touch the electric fence does not statistically significantly differ from the national average.

b. Fail to reject the null hypothesis and reject the research/alternative hypothesis. 3. a. Though we are comparing the sample mean with the population mean, since the

population standard deviation is not know and the sample standard deviation is known, a Dependent Sample t test is most appropriate |3.75| t obtained > 2.042 t critical (alpha = .05) for df of 35 (n-1; thought we use the value tabled for the more conservative df of 30, since no critical values are reported for 35 degrees of freedom in Appendix 2); thus, the average amount of money sorority members spend on clothes in a given month is significantly different from the average amount of money spent by all the women attending All-American U. That is sorority members spend significantly more money than other women attending the All-American U.

b. Highest level of significance achieved; = .001 c. Reject the null hypothesis and fail to reject the research/alternative hypothesis.

35

d. 3.75 t obtained (we dont use the absolute value here, because the direction of the relationship matters) > 1.697 t critical (alpha = .05, one tailed) for df of 35 (n-1; again we actually use the values of the more conservative 30 degrees of freedom). The highest level of significance achieved is = .0005. Thus, with a one tailed hypothesis, these differences are found to be even more significant (were are more confident the differences are meaningful)

4. a. The most appropriate test is the Independent Sample t test, given that you are asked to compare two sampled groups (independent samples). |4.8762| t obtained > 3.725 t critical (alpha = .001) for df of 25 (n1 + n2 2); thus, the average number of alcoholic beverages consumed per week by All-American U students is significantly different from the average obtained from All American State University students. In other words, students at All-American U drink significantly more than All American State University students.

b. The highest level of significance achieved is = .001. c. Reject the null hypothesis and fail to reject the research/alternative hypothesis. d. 4.8762 t obtained > 1.708 t critical (alpha = .05, one tialed) for df of 25 (n1 + n2 2). The highest level of significance achieved with the one tailed test is = .0005.

Thus, with a one tailed hypothesis, these differences are found to be even more significant (were are more confident the differences are meaningful)

5. a. The most appropriate test is the Independent Sample t test, given that you are asked to

compare two sampled groups (independent samples). |2.8743| t obtained > 2.485 t critical (alpha = .02) for df of 25 (n1 + n2 2); thus the average number of parties per semester that All-American U students attend is significantly different from the number of parties attended by students at All American State Univeristy. In other words, students at All-American U attend significantly more parties than All American State University students.

b. The highest level of significance achieved is = .01 (2.787 t critical for df of 25). c. Reject the Null Hypothesis and Fail to Reject the Alternative/Research Hypothesis.

d. 2.8743 t obtained > 1.708 t critical (alpha = .05, one tailed) for df of 25 (n1 + n2 2), but we must Reject the Alternative/Research Hypothesis, Fail to Reject the Null Hypothesis, and conclude that All-American U students do not attend significantly fewer parties than Students at All American State University because the t obtained is not negative. That is, though the absolute difference between the values is meaningful, it is not in the predicted direction.

6. a. The most appropriate test is the Difference t test, because we are asked to compare two

sets of scores obtained from a single group of people. |-3.0104| t obtained > 2.306 t critical (alpha = .05) for df of 8 (n-1); thus, the number of pages read per night while listening to country music was statistically significantly different from the number of pages read without any music. More specifically, listening to this type of music significantly decreases the number of pages read per night, compared to reading without music. b. The highest level of significance achieved is = .02 (2.896 t critical for df of 8)

36

c. Reject the Null Hypothesis and Fail to Reject the Alternative Hypothesis. d. |-3.0104| t obtained > 1.860 t critical (alpha = .05, one tailed) for df of 8 (n-1); The highest level of significance achieved with a one tailed test is = .01.

Thus, with a one tailed hypothesis, these differences are found to be even more significant (were are more confident the differences are meaningful)

7. a. The appropriate test is the Difference t test, because we are comparing two sets of

scores taken from a single group of people |-1.9174| t obtained < 2.201 t critical (alpha = .05) for df of 11 (n1); thus, the number of pages read per night while listening to the Blues does not statistically significantly differ from the number of pages read per night without music. More specifically, while listening to the Blues does appear to increase the number of pages read, compared to reading without music, the difference is not statistically meaningful. b. The highest level of significance achieved is = .10 (1.796 t critical for df of 11), but this does not meet accepted standard of .05. c. Fail to Reject the Null Hypothesis and Reject the Alternative Hypothesis. d. |-1.9174| t obtained < 1.796 t critical (alpha = .05, one tailed) for df of 11 (n1); The highest level significance achieved with a one tailed test is = .05.

Thus, while the difference between the two sets of reading scores was not significant using the more stringent non-directional one-tailed test, the decrease in the number of words read while listening to blues music, compared to reading with no music, is considered meaningful.

Exam/Quiz Questions 1. Using Cartoon 9.2 as a backdrop, lets say we want to know if the women at your university/college spend more or less money per month on clothes than compared to the national average amount spent by university/college women. We find the following: = $60.00 x-bar = $50.00 = $22.00 n = 49 a. Using the appropriate test (alpha = .01), are the averages statistically different? b. What does this tell us in the context of the null/research hypothesis? 2. Lets say we want to know if the professors at your university/college spend more or less money per month on clothes than compared to the national average amount spent by university/college professors. We find the following: = $50.00 x-bar = $65.00 s= $25.00 n = 25 (continued on next page)

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a. Using the appropriate test (alpha = .02) are the averages statistically different? b. What does this tell us in the context of the null/research hypothesis? c. What is the highest level of significance reached?

d. Perform a one tailed test (alpha = .05). Is it significant? What is the highest level of significance achieved?

3. Lets say we now want to know if social science majors spend more or less money on clothes than business majors. We draw two independent samples of students--1) from social science majors, and 2) from business majors--and find the following. x-bar1 = $44.00 x-bar2 = $53.00 s1 = $10.00 s2 = $8.00 n1 = 11 n2 = 9 a. Using the appropriate test (alpha = .05) are the averages statistically different? b. What does this tell us in the context of the null/research hypothesis? c. What is the highest level of significance reached?


4. Lets say we want to know if a presons graduating increases the amount of money spent monthly on clothes. We sample 9 students six months before graduation, and then three months after graduating. Our findings are report below. Individual Before After 1 $42.00 $55.00 2 $33.00 $40.00 3 $55.00 $52.00 4 $50.00 $60.00 5 $70.00 $65.00 6 $35.00 $55.00 7 $39.00 $48.00 8 $48.00 $56.00 9 $62.00 $63.00

a. Using the appropriate test (alpha = .05) does graduating have a statistically significant effect on the amount of money spent monthly on clothes? What sort of effect does it have?

b. What does this tell us in the context of the null/research hypothesis? c. What is the highest level of significance reached?


38

5. If a scientist collected information from a sample and compares it to information from a population and finds there is a significant difference between the sample mean and the population mean, but in reality there is no difference, then that researcher has committed ......

A. A Type I Error B. A Type II Error 6. In terms of the Standard Error of the Mean for a Z-Test, increasing the sample size does what to

the Z-Obtained. A. Increase the Standard Error of the Mean and increase the Z-Obtained. B. Increase the Standard Error of the Mean and decrease the Z-Obtained. C. Decrease the Standard Error of the Mean and increase the Z-Obtained. D. Decrease the Standard Error of the Mean and Decrease the Z-Obtained. 7. In terms of the Degrees of Freedom for an Independent Samples t-Test, increasing the sample size

of one group will do what to the t-Critical. A. Increase the Degrees of Freedom and Decrease the t-Critical. B. Increase the Degrees of Freedom and Increase the t-Critical. C. Decrease the Degrees of Freedom and Decrease the t-Critical. D. Decrease the Degrees of Freedom and Increase the t-Critical. 8. If a teacher wanted to know if using cartoons in class really makes students more interested in

class discussions and the teacher has good reason to believe that they wouldn't make students any less interested, then s/he would be justified in using which t-Critical for hypothesis testing?

A. One-Tailed B. Two-Tailed 9. If a scientist collects information from a sample, compares it to a population, and finds there is

not a significant difference between the sample mean and the population mean, but in reality there is a difference, then the researcher has committed.......

A. A Type I Error B. A Type II Error 10. After conducting an independent sample t test, if a researcher finds the results were not

significant, then what could s/he do so that the results might come out significant. A. Change from a one tailed to a two tailed test. B. Change form a Two tailed to a One tailed test. C. Increase the Sample Size. D. Decrease the Sample Size. E. Both B and C F. Both A and D

39

Chapter 10

Simple Regression and Correlation

Answers to Practice Exercises 1. a. Scattergram suggests a positive linear relationship

Complaints and Venison Data

02468

1012141618

0 5 10 15

Complaints

Num

ber T

urne

d in

to

Veni

son

b. a (y-intercept) = .6756; b (slope) = 1.1235.

(Note: in the homework directions asks us to find the slope (a) and the intercept (b), this is mislabeled. Slope should be (b) and the intercept should be (a). We have used the correct labels in these answers.)

c. Due to the limitations of the word-processing program used, the plotted least-squares regression line for this question is not included. Please see the main text for an example. The calculations for the expected values of Y are presented below. Y = bx + a Y = (1.1235)x + .6756 Y = Y = X = 1; (1.1235)(1) + .6756 = 1.7991 X = 9; (1.1235)( 9) + .6756 = 10.7871 X = 2; (1.1235)(2) + .6756 = 2.9226 X = 10; (1.1235)(10) + .6756 = 11.9106 X = 3; (1.1235)(3) + .6756 = 4.0461 X = 11; (1.1235)(11) + .6756 = 13.0341 X = 4; (1.1235)(4) + .6756 = 5.1696 X = 12; (1.1235)(12) + .6756 = 14.1576 X = 5; (1.1235)(5) + .6756 = 6.2931 X = 13; (1.1235)(13) + .6756 = 15.2811 X = 6; (1.1235)(6) + .6756 = 7.4166 X = 14; (1.1235)(14) + .6756 = 16.4046 X = 7; (1.1235)(7) + .6756 = 8.5401 X = 15; (1.1235)(15) + .6756 = 17.5281 X = 8; (1.1235)(8) + .6756 = 9.6636

40

d. r = .9107.

e. 6.9704 t obtained > 4.587 t critical (alpha = .001) for df of 10 (n 2); thus, statistically significant. Here we have reported the highest level of significance achieved.

f. Apparently, an increase in complaints leads to an increased number reindeer becoming venison. 2. a. Scattergram suggests a negative linear relationship

Age and Complaints

0

5

10

15

20

25

0 2 4 6 8 10 12

Age of Reindeer

Num

ber T

urne

d in

to

Veni

son

b. a (y-intercept) = 18.1863; b (slope) = -1.2469.


c. Due to the limitations of the word-processing program used, the plotted least-squares regression line for this question is not included. Please see the main text for an example. The calculations for the expected values of Y are presented below. Y = bx + a Y = (-1.2469)x + 18.1863 Y = Y = X = 1; (-1.2469)(1) + 18.1863 = 16.9394 X = 6; (-1.2469)( 6) + 18.1863 = 10.7049 X = 2; (-1.2469)(2) + 18.1863 = 15.6925 X = 7; (-1.2469)( 7) + 18.1863 = 9.4580 X = 3; (-1.2469)(3) + 18.1863 = 14.4456 X = 8; (-1.2469)( 8) + 18.1863 = 8.2111 X = 4; (-1.2469)(4) + 18.1863 = 13.1987 X = 9; (-1.2469)( 9) + 18.1863 = 6.9642 X = 5; (-1.2469)(5) + 18.1863 = 11.9518 X = 10; (-1.2469)(10) + 18.1863 = 5.7173

d. r = -.8239

e. |-4.1117| t obtained > 3.355 t critical (alpha = .01) for df of 8 (n 2); thus, statistically significant. Here we have reported the highest level of significance achieved.

41

f. Apparently, the younger the reindeer, the more complaints they make. Or, alternatively, as a reindeer ages they make fewer complaints. 3. a. Scattergram suggests a rather small positive linear relationship

Complaints and Elves Kicked

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16

Complaints

Num

bero

of E

lves

Kic

ked

b. a (y-intercept) = 3.737 b (slope) = .1966


c. Due to the limitations of the word-processing program used, the plotted least-squares regression line for this question is not included. Please see the main text for an example. The calculations for the expected values of Y are presented below. Y = bx + a Y = (.1966)x + 3.737 Y = Y = X = 1; (.1966)(1) + 3.737 = 3.9336 X = 8; (.1966)( 8) + 3.737 = 5.3098 X = 2; (.1966)(2) + 3.737 = 4.1302 X = 9; (.1966)( 9) + 3.737 = 5.5064 X = 3; (.1966)(3) + 3.737 = 4.3268 X = 10; (.1966)(10) + 3.737 = 5.7030 X = 4; (.1966)(4) + 3.737 = 4.5234 X = 11; (.1966)(11) + 3.737 = 5.8996 X = 5; (.1966)(5) + 3.737 = 4.7200 X = 12; (.1966)(12) + 3.737 = 6.0962 X = 6; (.1966)(6) + 3.737 = 4.9166 X = 13; (.1966)(13) + 3.737 = 6.2928 X = 7; (.1966)(7) + 3.737 = 3.9336 X = 14; (.1966)(14) + 3.737 = 6.4894 d. r = .2611

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e. |.8552| t obtained > 2.228 t critical (alpha = .05) for df of 10 (n 2); thus, statistically non-significant. f. The number of complaints received in a given moth does not meaningfully predict the number of elves that Santa will kick.

4. a. Scatterplot suggests that a curvilinear relationship exists.

Toys Asked for and Elves Kicked

0

2

4

6

8

10

12

14

0 5 10 15

Number of toys asked for each Month

Num

ber o

f Elv

es K

icke

d

Series1

b. a (y-intercept) = 6.4409; b (slope) = .0892


c. Due to the limitations of the word-processing program used, the plotted least-squares regression line for this question is not included. Please see the main text for an example. The calculations for the expected values of Y are presented below. Y = bx + a Y = (.0892)x + 6.4409 Y = Y = X = 0; (.0892)(0) + 6.4409 = 6.4409 X = 7; (.0892)( 7) + 6.4409 = 7.0653 X = 1; (.0892)(1) + 6.4409 = 6.5301 X = 8; (.0892)( 8) + 6.4409 = 7.1545

X = 2; (.0892)(2) + 6.4409 = 6.6193 X = 9; (.0892)( 9) + 6.4409 = 7.2437 X = 3; (.0892)(3) + 6.4409 = 6.7085 X = 10; (.0892)(10) + 6.4409 = 7.3329 X = 4; (.0892)(4) + 6.4409 = 6.7977 X = 11; (.0892)(11) + 6.4409 = 7.4221 X = 5; (.0892)(5) + 6.4409 = 6.8869 X = 12; (.0892)(12) + 6.4409 = 7.5113 X = 6; (.0892)(6) + 6.4409 = 6.9761

d. r = .0939 e. |.2982| t obtained > 2.228 t critical (alpha = .05) for df of 10 (n 2); thus, statistically non-significant.

43

f. The number of toys requested in a given moth does not meaningfully predict the number of elves that Santa will kick (at least not in a linear manner).

5. Note: This problem is quite difficult to solve when the table of critical values for r is not available, so you may choose not to assign this problem. However, we have provided a table of critical values for r (below) that you may wish to use for evaluating the significance of correlations, rather than using the r to t conversion procedure. Problem 3 and Problem 4 had non-significant correlations.

- For Problem 3, a correlation of .2611 would be significant at the .05 level if we had approximately 60 degrees of freedom (df) and therefore 62 subjects.

- For Problem 4, a correlation of .0939 would be significant at the .05 level if we had stubstantially more than 120 degrees of freedom (df), however we dont know for sure as, the table does not report critical values for more than 100 degrees of freedom. (A rough estimate would be about 300 subjects would be needed).

44

Table of Critical Values for Pearsons r

Level of Significance for a One-Tailed Test .10 .05 .025 .01 .005 .0005 Level of Significance for a Two-Tailed Test df .20 .10 .05 .02 .01 .001

1 0.951 0.988 0.997 0.9995 0.9999 0.99999 2 0.800 0.900 0.950 0.980 0.990 0.9993 0.687 0.805 0.878 0.934 0.959 0.9914 0.608 0.729 0.811 0.882 0.917 0.9745 0.551 0.669 0.755 0.833 0.875 0.951

6 0.507 0.621 0.707 0.789 0.834 0.9257 0.472 0.582 0.666 0.750 0.798 0.8988 0.443 0.549 0.632 0.715 0.765 0.8729 0.419 0.521 0.602 0.685 0.735 0.847

10 0.398 0.497 0.576 0.658 0.708 0.823 11 0.380 0.476 0.553 0.634 0.684 0.80112 0.365 0.457 0.532 0.612 0.661 0.78013 0.351 0.441 0.514 0.592 0.641 0.76014 0.338 0.426 0.497 0.574 0.623 0.74215 0.327 0.412 0.482 0.558 0.606 0.725

16 0.317 0.400 0.468 0.542 0.590 0.70817 0.308 0.389 0.456 0.529 0.575 0.69318 0.299 0.378 0.444 0.515 0.561 0.67919 0.291 0.369 0.433 0.503 0.549 0.66520 0.284 0.360 0.423 0.492 0.537 0.652

21 0.277 0.352 0.413 0.482 0.526 0.64022 0.271 0.344 0.404 0.472 0.515 0.62923 0.265 0.337 0.396 0.462 0.505 0.61824 0.260 0.330 0.388 0.453 0.496 0.60725 0.255 0.323 0.381 0.445 0.487 0.597

26 0.250 0.317 0.374 0.437 0.479 0.58827 0.245 0.311 0.367 0.430 0.471 0.57928 0.241 0.306 0.361 0.423 0.463 0.57029 0.237 0.301 0.355 0.416 0.456 0.56230 0.233 0.296 0.349 0.409 0.449 0.554

40 0.202 0.257 0.304 0.358 0.393 0.49060 0.165 0.211 0.250 0.295 0.325 0.40812

0 0.117 0.150 0.178 0.210 0.232 0.294 0.057 0.073 0.087 0.103 0.114 0.146Adapted from Appendix 2 (Critical Values of t) using the square root of [t2/(t2 + df)] Note: Critical values for Infinite df actually calculated for df= 500.

45

Exam/Quiz Questions 1. The below data set is indirectly in reference to Cartoon 10.1. As labeled, the independent variable represents the given elfs years of employment at the North Pole while the dependent variable represents each elfs monthly complaints about his/her boss--Santa. Years X Number of Y Employed Complaints 2 2 1 2 4 3 7 6 5 4 2 1 8 9 5 6

a. Construct a scattergram for this data. What sort of relationship appears to exist between years employed and complaints?

b. Calculate the slope and the y-intercept for this data. c. Plot the least-squares regression line for this data. d. Calculate the Pearsons-r correlation coefficient for this data. e. Using the appropriate t test, determine if the relationship between years employed and complaints is statistically significant. f. Having made all of the above calculations, what can we conclude about the relationship between years employed and complaints? (Note: for exams or quizzes where time is short, you may wish to provided you students with the values of the X, Y, XY, X2, and Y2, rather than providing the raw data) 2. Pearson-Product Moment Correlations (i.e., Pearsons r) allow us to measure the association between which types of Variables?

A. Nominal and Interval/Ratio C. Interval/Ratio and Interval/Ratio B. Nominal and Ordinal D. None of these 3. Which of the following is NOT true. A. Almost all research is based on the notion of trying to show causality. B. Causality can be absolutely proven with correlational data. C. Causality is the notion that one event or series of events causes another event(s) to occur. D. The Independent Variable is viewed as the hypothetical cause of the Dependent Variable.

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4. Which of the following examples demonstrates a Negative Linear Relationship (irrespective of whether the relationship is statistically significant).

A. As the amount of beer consumed increases, the intensity of the hangover increases. B. As the number of bowls of 3 alarm chili consumed decreases, the number of gastrointestinal anomalies experienced decreases. C. As the number of years of college attended increases, the strength of feelings of anxiety and despair about one's future life increases. D. As the Amount of THC consumed increases, the length of attention span decreases.

5. Assume that a researcher discovered that there was a significant positive correlation between snorting Jello up ones nose and having hallucinations involving Nancy Reagan and a talking Manatee bowling for dollars with Malcolm X. The results of this study could be interpreted in which of the following ways?

A. Snorting Jello Causes Hallucinations B. Hallucinations Causes Jello Snorting

C. Some other unmeasured variable is responsible for the association between Jello Snorting and Hallucinations

D. All of these are potential interpretations E. None of these are potential interpretations 6. The amount of variance shared by two variables is called _________. A. Unexplained Variance C. Error Variance B. Residual Variance D. Covariance 7. The statistic that tells us the percent of variance in one variable that is accounted for (explained by) variance in a second variable is called ________________.

A. Covariance C. Coefficient of Determination B. Residual Variance D. Correlation Coefficient 8. Which of the following correlation coefficients demonstrates the strongest relationship between two variables.

A. .01 B. -. 85 C. .53 D. -.01 9. Of the scattetplots (scattergrams) below, which represents the Strongest Correlation.

A. B. C.

47

Chapter 11

One-Way Analysis of Variance (ANOVA)

Answers to Practice Exercises 1. a. SS Between = 277.0884; SS Within = 84.75; TOTAL SS = 361.8334; df Between = 2; df Within = 21; TOTAL df = 23; MS Between = 138.5417; MS Within = 4.0357 F = 34.329; p < .01. [F crit. for df of 2 & 21 = 3.47 (.05) and 5.78 (.01)]. b. Yes. Because the F obtained is larger than the F critical. 2. * Group 1 versus Group 2 = t obtained 5.6003 > 2.831 t critical (alpha = .01; 21 df); this, significant. * Group 1 versus Group 3 = t obtained 8.0894 > 2.831 t critical (alpha = .01; 21 df); thus, significant.

* Group 2 versus Group 3 = t obtained 2.489 < 2.831 t critical (alpha = .01; 21 df) thus, not significant. (Though, you would find it to be significant at the less stringent .05 level).

3. SS Between = 30; SS Within = 380; TOTAL SS = 410; df Between = 1; df Within = 38; TOTAL df = 39; MS Between = 30; MS Within = 10; F = 3; Not Significant. [F crit. 1 & 38 = 4.10 (.05) and 7.35 (.01)]. 4. SS Between = 4800; SS Within = 14440; TOTAL SS = 19200; df Between = 3;

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df Within = 36; TOTAL df = 39; MS Between = 1600; MS Within = 400; F = 4; p < .05. [F crit. 3 & 36 = 2.86 (.05) and 4.38 (.01)]. 5. SS Between = 42; SS Within = 90; TOTAL SS = 132; df Between = 2; df Within = 30; TOTAL df = 32; MS Between = 21; MS Within = 3; F = 7; p < .01. [F crit. 2 & 30 = 3.32 (.05) and 5.39 (.01)]. 6. * Group 1 versus Group 2 = t obtained 7.4475 > 2.042 t critical (alpha = .05; 21 df); this, significant. * Group 1 versus Group 3 = t obtained 14.895 > 2.042 t critical (alpha = .05; 21 df); thus, significant. * Group 2 versus Group 3 = t obtained 7.4475 > 2.042 t critical (alpha = .05; 21 df) thus, significant. Exam/Quiz Questions 3. (15 pts) Assume that a researcher (of questionable sanity) wanted to evaluate the effects of poring single-malt scotch down the back of randomly selected ducks on the degree to which the ducks crave haggis, a traditional Scottish meat dish. The researcher identifies a single brand of scotch to test and selects three varieties which have been aged either 10 yrs (group 1), 20 yrs (Group 2) or 30 years (group 3). S/He gathers 27 ducks and randomly assigns then to the 3 different groups. The dependent variable here is the number of times the ducks peck the haggis, in the hour after exposure to the schotch. Preform an ANOVA test including the appropriate follow up tests (if suggested by the results). Be sure to include the highest level of significance reached and to construct an ANOVA summary table on which to present your results. The Sums of the Raw Data are as follows:

Group1 .1 = 75

.12 = 705 n1 = 9

Group 2 .2 = 30

.22 = 180 n2 = 9

Group3 .3 = 48

.32 = 318 n3 = 9

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2. The ANOVA test allows us to test the relationship between what kinds of variables? A. Nominal and Interval/Ratio C. Interval/Ratio and Interval/Ratio B. Nominal and Nominal D. None of these 3. If an experimenter is going to test the differences that exist between 8 groups of subjects,

how many individual comparisons must be tested. A. 28 B. 21 C. 10 D. 8 4. If an experimenter conducts 10 individual independent-sample t-tests each at the .05

alpha level, without using an ANOVA procedure first, then what is true probability of committing a Type I Error for all 10 tests combined?

A. 5% B. 50% C. .5% D. 25% (note, the text does not explicitly present the formula for calculating this per-experiment error rate, so be cautious about using this item unless you have covered it in class). 5. If a researcher preforms an ANOVA test using only 2 groups of subjects then essentially

s/he has preformed which of the following tests? A. A t-test C. A Correlation B. A Simple Linear Regression D. None of these 6. In a case where we have 3 groups, where ANOVA statistic (F) is found to be significant,

which of the following is NOT reasonable to conclude. A. We should Reject the Null Hypothesis. B. We should Fail to Reject the Research Hypothesis. C. Group 1 and 3 are significantly different. D. We should perform more tests.

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Chapter 12

Factorial Analysis of Variance Answers to Practice Exercises 1. Main effects describe the relationship between a single independent variable and dependent variable. These are nearly the same as the F obtained from the One-Way Anova. 2. Interaction effects represent the combined influence two independent variables on a dependent variable. A significant interaction indicates that the strength and/or direction of the relationship between one IV and a DV, depends on the value of the remaining IV. 3. The main effect of an independent variable for a given dependent in factorial ANOVA is generally larger than if we tested the same independent and dependent variable were test in a One-Way ANOVA, because the error term (MS error) is generally smaller in the Factorial ANOVA. MS error in the factorial ANOVA is generally smaller, because part of it gets accounted for by the other Independent Variables included in the analysis. 4. a. No main effect for IV 1; the main effect for IV 2 and the interaction are possibly

significant. b. No main effect for either IV; the interaction effect is possibly significant. c. Main effect for IV 1 is possibly significant; No main effect for IV 2; No interaction. d. No main effects and no interation. e. Main effect for IV 1, main effect for IV 2 are possibly significant. No interaction. f. Main effect for IV 1, main effect for IV 2, and interaction are all possibly significant. g. Main effect for IV 1 and Interaction are possibly significant; No main effect for IV 2. h. No main effect for IV 1, No interaction effect; Main effect for IV 2 is possibly significant.

5 & 6. (Note: these are really only one question)

a. Step 1 = find X.jk and X2.jk

X.11 = 60 X2.11 = 738 X. 21 = 9 X2.21 = 31 X.12 = 9 X2.12 = 39 X.22 = 59 X2.22 = 699

Step 2 = find X.j. and X2.j.

X.1. = 69 X2.1. = 777 X.2. = 68 X2.2. = 730 Step 3 = find X..k and X2..k

X..1 = 69 X2..1 = 769 X..2 = 68 X2..2 = 738

Step 4 = find n.jk, n.j., and n..k n.11 = 5 n.21 = 5 n.12 = 5 n.22 = 5 n.1. = 10 n.2. = 10 n..1 = 10 n..2 = 10

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Step 5 = Find Xijk = 137 Step 6 = Find X2.jk = 1507 Step 7 = Find nijk = 20 Step 8 = (Xijk)2/nijk = 938.45 Step 9 = SStot = 568.55 Step 10 = SSIV1 = .05 Step 11 = SSIV2 = .05 Step 12 = SSbtw tot = 510.15 Step 13 = SS1x2 = 510.05 Step 14 = SSerror = 58.4 The remaining steps are summarized in the Anova Summary Table below.

SS df MS F p Main Effects

IV 1 .05 1 .05 .0136 p > .05, ns IV 2 .05 1 .05 .0136 p > .05, ns

Interaction 1x2 510.05 1 510.05 139.7397 p < .01

ERROR 58.40 16 3.65 TOTAL 568.55 19

b. Neither Main effect is significant.

- The average number of curse words used during the interview was the essentially the same for participants who viewed South Park and participants who viewed the Cosbey Show.

c. The interaction effect is significant. Among participants who watched South Park, participants who believe curse words are actually cursed (or at least rightfully taboo) cursed more than South Park viewers that do not believe in curse words. The opposite pattern was found among Cosbey Show viewers. Cosbey Show viewers who do not believe that curse words are actually cursed used fewer curse words than those who do not believe in curse words. d.

02468

101214

South Park Cosbey Show

Cursed

Not-Cursed

52

7 & 8. (Note: these are really only one question) a. Step 1 = find X.jk and X2.jk

X.11 = 56 X2.11 = 650 X. 21 = 26 X2.21 = 114 X.12 = 89 X2.12 = 1595 X.22 = 56 X2.22 = 650 X.13 = 54 X2.13 = 604 X.23 = 54 X2.23 = 590

Step 2 = find X.j. and X2.j.

X.1. = 199 X2.1. = 2849 X.2. = 136 X2.2. = 1384 Step 3 = find X..k and X2..k

X..1 = 82 X2..1 = 794 X..2 = 145 X2..2 = 2245 X..3 = 108 X2..3 = 1194

Step 4 = find n.jk, n.j., and n..k n.11 = 5 n.21 = 5 n.12 = 5 n.22 = 5 n.13 = 5 n.23 = 5 n.1. = 15 n.2. = 15 n..1 = 10 n..2 = 10 n..3 = 10

Step 5 = Find Xijk = 335 Step 6 = Find X2.jk = 4233 Step 7 = Find nijk = 30 Step 8 = (Xijk)2/nijk = 3740.8333 Step 9 = SStot = 492.1667 Step 10 = SSIV1 = 132.2999 Step 11 = SSIV2 = 200.4667 Step 12 = SSbtw tot = 399.3667 Step 13 = SS1x2 = 66.6001 Step 14 = SSerror = 92.8000 The remaining steps are summarized in the Anova Summary Table below.

SS df MS F p Main Effects

IV 1 132.2999 1 132.2999 34.2160 p < .01 IV 2 200.4667 2 100.2333 25.9228 p < .01

Interaction 1x2 66.6001 2 33.3005 8.6123 p < .01

ERROR 92.8000 24 3.8666 TOTAL 492.1667 29

b. Both Main effects are significant.

Main effect for Food Type

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02468

10121416

Pick

les

& S

pam

Man

go &

Gua

c

Mac

kere

l&

Bac

on

Food Type

- Though the main effect for food type is significant, it does not necessarily tell us which groups are different. To determine which groups are significantly different from one another, we would need to perform follow-up tests like the LSD test presented in chapter 11. If you do so, you will find that the all three groups are different from one another. Thus we can conclude that, people primed with wearing Mangos in their ears and Guacamole mustaches performed the relevant acts significantly more often than either of the other groups (mean = 14.5). People primed with wearing Mackerel in their pants and a Canadian Bacon necklace performed the relevant act significantly more often (mean = 10.8), compared to the Pickles and Spam group (mean 8.2). Main Effect for Stimulus Duration

02468

101214

100 ms 1000 ms

Line 1

- The significant main effect for stimulus type indicates that people were more likely to wear food items after receiving subliminal primes of 100 ms (mean = 13.2667), compared to the food wearing behavior of people primed in a more obvious manner (1000 ms; mean = 9.0666).

c. The interaction effect is significant. Among participants who were primed subliminally, it appears that the Mongo & Guacamole prime was most effect in eliciting food wearing behavior. Also, Pickles & Spam and Mackerel & Bacon primes seemed to be equally effective at influencing food wearing behavior, when subliminal primes are used. With respect to slower, non-subliminal primes, the Pickles & Spam prime resulted in less food wearing behavior, compared to Mangos & Guac and Mackerel & Bacon. People primed with Mackerel and Bacon did not differ in their food wearing behavior. It is interesting to note that both the Pickles & Spam prime and the Mangos & Guac prime

54

resulted in more frequent food wearing behavior when the primes were presented in subliminal manner, compared to the slower, 1000 ms primes. However, the Mackerel and Bacon prime seemed to be equally effective, regardless of the speed at which the prime was presented. d.

0

5

10

15

20

Pickles& Spam

Mango &Guac

Mackerel& Bacon

100ms1000ms

Exam\Quiz Questions 1. If you have two discrete Independent Variables, and a Continuous Dependent Variable, then which of the following statistics should be used to test their association. a. 2 b. Pearsons r c. t-test d. One-Way ANOVA e. Factorial ANOVA 2. Mr. Hat is testing the effects of different drug dosages (10 mg/kg, 100 mg/kg, or 1000 mg/kg) on the aggressive behavior of vicious wild bunny rabbits. Also, the researcher wants to know whether the rabbits sex influences their aggressive behavior. Which of the following designs best describes this study? a. 2 x 2 b. 3 x 3 c. 3 x 2 d. 2 x 2 x 2 3. How many conditions (groups) would have to be created in a 3 x 4 x 3 design. a. 10 b. 36 c. 21 d. 100 4. In a complex (i.e. factorial) design, the overall effect of an independent variable on the dependent variable is referred to as which of the following? a. Main Effect b. Simple Effect c. Interaction Effect d. Complex Effect 5. When we say the at the influence of one variable depends on the influence of another variable, then we are talking about which of the following? a. Main Effect b. Simple Effect c. Interaction Effect d. Complex Effect 6. In general, which of the following F statistics will be larger? a. the Main effect tested using a One-Way Anova b. the Interaction Effect tested using a One-Way Anova c. the Main effect tested using a Factorial Anova d. the Main effect tested using an independent sample t test

55

Use the Figure Below to Answer questions 10 - 13. Use labeled parts of the figure (A - F) to answer the questions 7. Which part(s) represents the MS between for IV 1 ____________ 8. Which part(s) represents the MS between for IV 2 ____________ 9. Which part(s) represents the MS error __________

10. Which part(s) represents the MS between for the Interaction ___

Problems (11- 18) Use the graphs provided to answer the following questions. Indicate Yes or No as to whether the table represents Main and/or interaction effects for two variables

56

19. The data below refers to a 2(sex) x 4 (TV Condition; Southpark, Saved by the Bell, Dukes of Hazard, and Love Boat) Anova, with 180 participants, that tests the association between sex, TV exposure and attitudes toward a receiving a Swedish massage from Barbara Bush. Complete the Anova table to find the missing Fs. Source SS df MS F p Main Effects Sex IV1 4.4567 ____ TV Condition IV2 5.6789 ______ ____ Interaction Effect Sex X TV Condition 1 x 2 6.8901 ____ Error Total 72.3065 179

57

Chapter 13

An Introduction to Chi-Square and Other Non-Parametric Statistics

Answers to Practice Exercises 1. a. Chi-square obtained = .0478 < 3.84 (.05) 6.63 (.02) Chi-square critical values; thus, NOT significant. 2. a. After determining that the mean is 10.5 and reformatting the data into a 2 X 2 contingency table finds: Chi-square obtained = .1435 < 3.84 (.05) 6.63 (.01) Chi-square critical values; thus, NOT significant. 3. a. Mann-Whitney U obtained = 1.3044 < 1.96 Z critical (.05); thus, NOT significant. Exam/Quiz Questions 1. Chi square statistics are predominantly used for what types of data A. Ordinal & Ratio C. Ordinal & Continuous B. Nominal & Continuous D. Nominal Data 2. The results of a chi square test tells us that

A. The frequency of occurrence of different groups is significantly different from the frequencies expected by chance.

B. The Observed frequency of all groups is greater than the expected frequency. C. One group has a larger mean than any other group. D. The Observed frequency of all groups is less than the expected frequency. 3. E (O - E) = A. 0 C. 1 B. n D. None of these 4. In a two variable chi Square; E E = A. E O C. E R ( R = Row totals) B. n D. All of these 5. In a chi square with two variables, if V1 has 3 groups and V2 has 10 groups, then df = ____ .

A. 7 B. 18 C. 21 D. 30 6. Which of the following statistical tests allows researchers to test the association between an ordinal and nominal variable, by collapsing the ordinal variable into a nominal variable. A. The Chi Square B. The Medain Test C. the Mann-Whitney U

58

7. Which of the following statistical tests is the equivalent of a t - test, but is used when the assumptions of the population distribution might be violated or the sample size is very small? A. The Chi Square B. The Medain Test C. the Mann-Whitney U 8. Assume that a researcher wanted to test the long term effects of Bovine Parental Control Techniques on childrens disruptive behavior. The researcher focused on 3 categories of Control Techniques: Threats to take calves to McDonalds, Threats to take calves to Burger King, and one reward technique (a trip to Chick-Fil-a). The researcher asked parents what technique the parents most often used and the researchers recorded whether their children were disruptive or not during a 15 min car ride in a laboratory simulator. The data are presented below. Using the appropriate test, determine which, if any, control technique is most effective in reducing disruptive behavior. McDonalds Threat Burger King Threat Chick-Fil-a Reward Disruptive Yes 5 4 1 Disruptive No 3 2 5

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