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BIOSTATS 540 - Introductory Biostatistics

Fall 2018 Examination 1

Units 1&2 – Summarizing Data & Data Visualization Due: Wednesday October 10, 2018

Last Date for Submission with Credit: Wednesday October 17, 2018

Rules: This is an “open book” “take-home” exam. You are welcome to use any reference materials you wish. You are welcome to use the computer as you wish, too. However, you MUST work this exam by yourself and you may not consult with anyone. Instructions and Checklist

__1. Start each problem on a new page. __2. Write your name on every page __3. Make a copy of your exam for safekeeping (sometimes a mailed exam is lost!) __4. Submit a completed signature page (See next page).

How to submit your exam:

Worcester “in-class” Section: __1. Please email a pdf of your completed exam to class on Wednesday October 10, 2018 being sure that you have chosen a filename that includes your name! (note – exam1.pdf is not a good choice); OR __2. Mail your completed exam to me with post-mark October 10, 2018 to my address below. Blackboard Learn Online Section: __1. Upload your completed exam to the ASSIGNMENT tab no later than 11:59 pm on Wednesday October 10, 2018. This must be a single pdf ; OR __2. Mail your completed exam to me with post-mark October 10, 2018 to my address below.

Address and Telephone Number for Mailing

Carol Bigelow Biostatistics & Epidemiology/402 Arnold House University of Massachusetts/Amherst 715 North Pleasant Street Amherst, MA 01003-9304 Tel. 413-545-1319



BIOSTATS 540 - Introductory Biostatistics Fall 2018

Examination 1 Units 1&2 – Summarizing Data & Data Visualization

Due: Wednesday October 10, 2018 Last Date for Submission with Credit: Wednesday October 17, 2018

Signature This is to confirm that in completing this exam, I worked independently and did not consult with anyone. Signature: ___________________________________________________________ Printed Name: _____________________________________________________ Date: ___________________________



1. (10 points total) The following table lists some variables that might be of interest in your next data analysis. For each variable, complete the associated table indicating whether it is categorical (and if so, is it nominal or ordinal) or quantitative (and if so, is it discrete or continuous). Categorical Quantitative Variable nominal ordinal discrete continuous

Example Eye color X 1a (1 point) How many hours you slept in the

past 24 hours

1b (1 point) Whether or not you have slept for at least 7 hours in the past 24 hours

1c (1 point) Number of Harry Potter books that you have read

1d (1 point) How many states in the United States you have visited

1e (1 point) Handedness (which hand you write with)

1f (1 point) Political viewpoint (classified as liberal, moderate, or conservative)

1g (1 point) Day of the week on which you were born

1h (1 point) Average study time per week 1i (1 point) How many birthday cards you

received on your last birthday

1j (1 point) Number of turkeys that visited your back yard during all of November last year.



2. (10 points total) This visualization is for questions 2a and 2b. The following dot plots display the distributions of daily high temperatures for the month of February 2006 in Lincoln, Nebraska; San Luis Obispo, California; and Sedona Arizona.

2a. (3 points) Which city tended to have the highest daily high temperatures in that month? Which city tended to have the lowest daily high temperatures in that month? In 1-2 sentences, explain your reasoning. 2b. (3 points) Which city had the most day-to-day consistency in daily highest temperatures in that month? Which city tended to have the lowest day-to-day consistency in daily highest temperatures in that month? In 1-2 sentences, explain your reasoning.



This visualization is for question 2c. A poll conducted by CNN, USA Today, and Gallup on September 8-11, 2005, asked people whether or not they thought race was a factor in the government’s slow response to Hurricane Katrina in New Orleans, USA. The following bar graphs compare the responses of blacks and whites. (Dear class, it’s a little hard to make out the “no opinion” bars but they are there, at the very top!)

2c. (4 points) Very briefly, comment on what these bar graphs reveal about the opinions of whites and blacks on whether or not race was a factor in the slow response to Hurricane Katrina. You may assume that the survey was well designed.



3. (10 points total) A very large international study of cardiovascular disease is the MONICA study. The table below shows a subset of the data. The sample size is n=40 and the reported data are measurements of age (AGE), alcohol use in the last week (ALC, coded as yes or no) and level of protein S (PROTS). It is of interest to learn if protein S levels vary with drinking in the last week.

3a. (5 points) By hand is fine or any other way if you prefer, construct two stem and leaf diagrams of protein S levels (PROTS), one for non-drinkers in the last week and one for drinkers in the last week.

3b. (5 points) (note - I am not asking for you to construct a plot here). A side-by-side box plot of protein S levels (PROTS) could be constructed to compare the distribution of PROTS, drinkers versus non-drinkers. To do this would utilize some of the following table of summary statistics. Complete the following table.

Non-Drinker Drinker

Number in group, n = P25 = Q1 = Lower Quartile =

P50 = Q2 = Median Quartile = P75 = Q3 = Upper Quartile = Interquartile Range (IQR) =

1.5* IQR= Value of Lower Fence = Value of Upper Fence =

Outliers (if any) below lower fence (LIST) = Outliers (if any) above upper fence (LIST) =



4. (10 points total) The following table lists length of stay in hospital (days) for a sample of 25 patients.

5 10 6 11 5 14 30 11 17 3 9 3 8 8 5 5 7 4 3 7 9 11 11 9 4

4a. (4 points) By hand, construct a frequency/relative frequency table for these data using 5-day class intervals. Include columns for the frequency counts, relative frequencies, and cumulative frequencies.

4b. (2 points)

What percentage of hospital stays were less than 5 days?

4c. (2 points)

What percentage of hospital stays were less than 15 days?

4d. (2 points)

What percentage of hospital stays were at least 15 days in length?



5. (10 points total) The Internal Revenue Service (For our international students – these are the US Tax folks!!) is interested in estimating its total revenues that will be obtained from income taxes. Towards this end, a random sample of n=15 tax returns is reviewed. The taxes paid for these 15 returns (in thousands of dollars) were

54 22 32 59 36 27 29 92 43 35 20 39 26 32 63

5a. (2 points) By hand, compute the mean.

5b. (2 points)

By hand, compute the median.

5c. (2 points)

Explain why the mean and median are so different.

5d. (2 points)

Estimate the total revenues to the government under the assumption that there are 75 million taxpayers.



6. (10 points total)

6a. (5 points) The following is a relative frequency table summarizing the score earned on a BIOSTAT 540 exam. By hand, compute the mean. (Tip – You have everything you need to do this; it just takes a little thinking.)

Exam I Score Relative Frequency 100 .40 88 .30 81 .20 76 .10

6b. (5 points) As the market continues to boom, some are concerned that we might soon suffer a recession. During recessions, average earnings typically go up. Drawing upon your understanding of what happens during a recession, explain how this can be.




7a. (5 points) Suppose the scores on a difficult exam have a sample mean of 67 and a standard deviation of 20. Suppose the instructor decides to boost each student’s score by 10 points; that is, the instructor adds 10 points to each student’s score. What are the values of the new sample mean and sample standard deviation?

7b. (5 points)

Next, suppose that the sample mean income for a group of workers is $59,000 with a standard deviation of $15,000. You are hired to report this information at a meeting in the U.K. If one British pound equals $2.25, what is the value of the sample mean and sample standard deviation in units of British pounds?




8a. (5 points) Consider the relationship between the standard deviation and the standard error. Suppose it is known that the standard deviation is 3. How large a sample n should be taken for the standard error of the mean to have a value of 0.5?

8b. (5 points) A scientist has just been funded by the National Institutes of Health to conduct a very expensive study. As it happens, the budget has been cut. Therefore, the choice of laboratory for analysis of sample data is being re-visited. Suppose the choice is between laboratory “A” and “B”. Laboratory “A” has a standard deviation of one milligram and each sample analysis costs $3. Laboratory “B” has a standard deviation of two milligrams but each sample analysis costs $1. All other things being equal, is the principal investigator better off spending $9 on laboratory “A” or spending $9 on laboratory “B”? Hint – This question is asking you to show me your understanding of standard error.



9. (20 points total) Dear BIOSTATS 540 Fall 2018: This question asks you to reflect on the interpretation of data summaries that are provided to you. How important! Again, there is not a worked homework problem that you can mimic to answer this question. Have no fear. You are asked to choose one of two questions (A or B) to answer. And, I am not looking for you to tell me specific things. Please note - You will get full credit for a thoughtful answer (whatever that might be) that does not have mistakes in interpretation. Choose EXACTLY ONE (A or B) Choice A - Choking on food is an important cause of accidental deaths in infants. The following table is a summary of infant deaths from choking on food in England and Wales, by year, for the years 1974-1985. Write a brief report (a paragraph or so, no more!) on these data that includes: (a) a summary of the facts given by the information in this table; and (b) some possible explanation for the decrease in deaths over time between 1979 and 1984.

Year

Number of Deaths

1974 126 1975 93 1976 97 1977 97 1978 90 1979 110 1980 74 1981 62 1982 41 1983 29 1984 30



Choice B - Age is a variable that is important in most if not all epidemiological studies of health because our health is so strongly related to age. The following table is a two-dimensional table that summarizes the distribution of age in a certain population every five years starting with 1970 (the first row) to 2000 (the last row). Each row contains information for one year. Reading across the row (over the column), the table shows the number of individuals in each age group. If you choose this option, please do the following: (a) using the data provided, produce a new two-dimensional table that shows, for each year, the percentage of that year’s total population in each age interval (Tip! In each row, the sum of your percentages should be 100%); and (b) write a brief report (a paragraph or so, no more!) on what these summaries suggest regarding the possibility (or lack thereof) of changes over time in the age distribution of this population.

Interval of Age, years

Year

0-4

5-14

15-44

> 44

Total

1970

1,400

3,000

8,000

7,600

20,000 1975 2,700 5,000 12,000 10,300 30,000 1980 4,600 9,000 15,000 11,400 40,000 1985 6,000 11,000 16,500 11,500 45,000 1990 8,000 12,000 18,000 12,000 50,000 1995 10,000 13,500 19,000 12,500 55,000 2000 11,500 15,000 20,500 13,000 60,000

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