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Final Exam Review Problems – Math 13 – Statistics – Summer 2013
These problems are due on the day of the final exam.
Name: (Please PRINT)
Problem 1:
(a) Find the following for this data set {9, 1, 5, 3, 6, 8, 8, 4, 3, 2, 1, 1, 8, 9, 7}
Mean Median: Mode: Range:
(b) Find standard deviation without using calculator for this data set:
{4, -6, 5, -7}
2
22
1
1
x xs
n
n x xs
n n
Problem 2: A couple wants to have three babies for the next three years, only one baby per year
(either boy or girl) and no other possibility.
Create a sample space, i.e. collection of all simple events:
Find the probability that they will have two girls and a boy.
Find the probability that they will have at least one girl.
Find the probability that they will have no more than two boys.
Find the probability that they will have no girls.
Find the probability that they will have between one and three girls.
Problem 3: Quality Control: As a quality control manager in a clothing company you randomly
select 5 shirts from a collection of 2000 shirts that just came to your company from Bangladesh.
You will reject all the shirts of if you find at least one faulty shirt. It is assumed that there are 20
faulty shirts in the lot of 2000 shirts. Find the probability of accepting all the shirts in this lot.
Problem 4: On the day of an important exam such as the SAT, you keep a backup mechanical
pencil in the event one fails so that you may use the other. Given that there is a 95% chance that
a mechanical pencil would work, what are your chances that you would not have to get a third
mechanical pencil at the test center at the expense of your precious exam time?
Problem 5: Permutation and combination: What are your chances of winning the Mega
Millions Lottery? In Mega Millions you pick 5 numbers from 1 to 56 without replacement and 1
number from 1 to 46.
Problem 6:Assume that you are investing $10,000 in one bond. There are two types of bonds
available. The first bond gives you a 7% return with a default rate of 3% and the second bond
gives you a return of 9% with a default rate of 5%. Which one these bonds would you consider
for investing your $10,000 assuming that you want to maximize your profit.
Problem 7: A new drug named CURAIDS that is 60% effective in extending the average life of
an AIDS patient by twenty years. Five randomly selected AIDS patients from Africa are treated
with this new drug. Answer the following questions based on the above information.
(a) Show that the above situation satisfies all four criteria for the Binomial probability
distribution.
(b) (10 points) Fill in the probabilities in the following table. Show your calculations.
x 0 1 2 3 4 5
P(x)
(c) What is the probability that no more than 4 patients are cured? Use results from part (b), do
not do the calculations again.
(d) Find the probability that more than 2 patients or less than or equal to 5 patients are cured.
Use results from part (b), do not do the calculations again.
(e) Find the probability that at least 4 patients are cured. Use results from part (b), do not do the
calculations again.
(f) Find probability that less than 2 or more than 3 patients are cured. Use results from part (b),
do not do the calculations again.
Problem 8: In a city named Dhaka there were 125 drug related crimes over one year period.
Find the probability that on a given day there will be exactly 3 drug related crimes in that city.
UsePoisson distribution. Explain the requirements for Poisson distribution.
( )!
x eP x
x
Problem 9: According to the U.N. report, the average yearly income in Bangladesh is about
$500/year. It is also estimated that the population standard deviation is $100. Find the following
probabilities:
a) If you randomly select a person find the probability that she/he would make between $400 and
$600.
b) If you randomly select 30 persons find the probability that their average yearly income would
be between $400 and $600.
Problem 10: (Normal Distribution)Assume that you are a restaurant owner. The customer
waiting time at your restaurant is normally distributed with an average waiting time of 12
minutes and a standard deviation of 3 minutes. You want to reward (with a free burger) 2% of
the customers who wait the longest amount of time. So what should you tell your customers
about minimum waiting period before they can get a free burger?
Problem 11: In a survey of 200 Hartnell students, it was found that 60 students said that English
was not their first language. Create a 95% confidence interval for true proportion of Hartnell
students whose first language is not English.
Assumptions:
Margin of error:
Graph:
Confidence interval:
Explanation of confidence interval:
Problem 12: Population proportion A Popular TV show named ROOTS that addressed the
black history and culture in the U.S. was very popular in the 1980s. You are curious if the
majority of the population nowadays have heard of this show or know about it. Your research
indicated that 241 people knew about this show out of 495 people you surveyed. Create a 95%
confidence interval for the true population proportion.
Assumptions:
Graph:
Margin of error:
Confidence interval and explanation:
Problem 13: t-distribution: Following table represents the number of hours 10 different
Hartnell College students work per week.
20 35 23 25 38 15 41 33 19 29
It is known that the distribution of the number of hours a HartnellCollege student works has
approximately bell shape. Create a 95% confidence interval for the true mean of the number of
hours per week a HartnellCollege student works.
Assumptions:
Calculations: / 2
x E x E
sE t
n
Graphs:
Confidence interval and explanation:
Problem 14: Assume that the distribution of average yearly salary for Hartnell College
graduates is a bell shaped curve. A random sample of 13 Hartnell College graduates has a mean
salary of $35,000 and a standard deviation of $5,000. Create a 95% confidence interval for the
population standard deviation.
Assumptions:
Calculations: 2 2
2
2 2
1 1
R L
n s n s
Graph:
Confidence interval and explanation:
Problem 15: It is known that in Bangladesh a person makes on the average $75 a month with a
standard deviation of $9. You, as a researcher, are interested in determining if the monthly
average income per person has increased. Therefore, you take a random sample of 100 people
and find that the sample average is $79. If you desire a significance level of 0.05, then state your
conclusion based on the calculations you make.
Assumptions:
Null and Alternative hypotheses:
Calculations: x
z
n
Graph and critical values:
Conclusions:
Problem 16: A Popular TV show named ROOTS that addressed the black history and culture in
the U.S. was very popular in the 1980s. You are curious if the majority (more than 50%) of the
population nowadays have heard of this show or know about it. Your research indicated that 241
people knew about this show out of 495 people you surveyed. What is your conclusion?
Significance level is 0.05.
Assumptions:
Null and Alternative hypotheses:
Calculations:p̂ p
zpq
n
Graph and critical values:
Conclusion:
Problem 17: Hypothesis Testing: 200 field workers were surveyed and their average yearly
income was $13,700. The population standard deviation for the income distribution of field
workers is assumed to be $4,000. Use the sample data, with 0.05 significance level, and test the
claim that average income for the population of field workers is different from $14,000 per year.
Requirements:
Null and Alternative Hypotheses:
Test Statistic: * xxz
n
Graph and critical regions:
Conclusion:
Problem 18: Hypothesis test: (Matched pair) An exercise program is claimed to be effective in
reducing weight. The following represents the weights of 8 people before and after the exercise
program. Is there sufficient evidence to support the claim that there is a difference in weights
before and after the program? Use a 0.05 significance level.
Before 150 135 191 210 189 123 132 175
After 148 136 172 192 185 120 135 170
Assumptions:
Null and alternative hypotheses:
Calculations:
* ddt
s
n
and degrees of freedom = n – 1
Graphs and critical points:
Conclusion:
Problem 19: Two population proportions inferences: According to the PEW Research Center for
the People & the Press in 2000 approximately 50% of the people surveyed said that the
immigrants strengthen the U.S. with their hard work and talents whereas in 2006 approximately
41% responded similarly. Let us assume that each year the survey was conducted on 2,000
randomly selected adults in the U.S. Based on this information would you conclude that there is
a progressively negative attitude towards immigrants in the U.S.? (Use significance level of 0.05,
i.e. 95% confidence level)
Assumptions:
Null and alternative hypotheses:
Calculations:
1 2 1 2*
1 2
1 2 1 21 2
1 2 1 2
ˆ ˆTest Statistic:
ˆ ˆwhere and and and 1
p p p pz
pq pq
n n
x x x xp p p q p
n n n n
Graphs and critical points:
Conclusion:
Create a confidence interval:
1 2 1 2 1 2
1 1 2 2/2
1 2
ˆ ˆ ˆ ˆ
ˆ ˆ ˆ ˆwhere margin of error:
p p E p p p p E
p q p qE z
n n
Problem 20: A 50-year long study by the British researchers shows that on the average smokers
live 10 years less than the nonsmokers do. You being the curious cat collected some data from a
reliable source and found that 621 smokers had average life span of 77 while 831 nonsmokers
had an average life of 71. You also have the information that the sample standard deviation for
life expectancy for both the smokers and nonsmokers is 10. Based on this information would
you reject the null hypothesis that there is no difference in the average life expectancy between
the smokers and nonsmokers?
Assumptions:
Null and alternative hypotheses:
Calculations:
1 2 1 2*
2 2
1 2
1 2
Test Statistic: x x
ts s
n n
Graphs and critical points:
Conclusion:
Problem 21: F-distribution: A new drug was tested on treatment population and placebo
population. Test the claim that variances for two populations differ. Significance level is 0.05.
Treatment group: sample size = 17, mean = 23.84, standard deviation = 2.31
Placebo group: sample size = 36, mean = 21.97, standard deviation = 2.01
Assumptions:
Null and alternative hypotheses:
Calculations: 2
* 1
2
2
Test Statistic: s
Fs
Graph and critical values:
Conclusion:
Problem 22: Following represents the amount of tips paid for different bills at a restaurant.
Bill (in $) 20 15 39 69 55 72 85 79
Tips (in $) 5 5 8 10 15 10 20 15
(a) Use hypothesis testing to determine whether there is linear correlation between the bill and
the tip paid?
*
21
2
rt
r
n
Degree of freedom (n – 2)
(b) Find the equation of the regression line for the above set of data.
(c) Predict tip for $95.
(d) Predict tip for $72
END OF FINAL EXAM REVIEW
Midterm 1 Review Problems – Math 13 – Statistics – Summer 2013
These problems are due on the day of the midterm.
Name: (Please PRINT)
Problem 1: Identify different levels of measurements for (a) through (d)
(a) Heights of buildings in the city of Salinas
Nominal Ordinal Interval Ratio
(b) Temperature on different days of the year in Salinas
Nominal Ordinal Interval Ratio
(c) Possible letter grades you may receive in the class
Nominal Ordinal Interval Ratio
(d) Names of 10 students from the class
Nominal Ordinal Interval Ratio
(e) Identify different types of sampling and data:
At a buffet they have different types of foods; these are American food, Asian food, Indian food,
and Italian food. You eat two items randomly from each category of food.
Convenience Systematic Stratified Clustering
(f) Determine if the following example represents discrete or continuous data:
Candy store sells candies only in the following amount: 0.2 lbs, 0.4 lbs, 0.6 lbs…
Continuous Discrete
(g) Many students are getting A’s in Mo’s Statistics class. Tom says Mo is a great teacher, while
Jessica says Mo is an easy grader. This situation is called:
Problem 2: Your grade in the class consists of 2 midterms 15% each, homework 10%, project
5%, attendance 10%, and final 30%. Find the weighted mean if your scores are as follows in the
class.
Midterm 1: 85
Midterm 2: 90
Final: 80
Homework: 95
Project: 100
Attendance: 75
Weighted Mean: w x
xw
Problem 3:
(a) Find the following for this data set {9, 1, 5, 3, 6, 8, 8, 4, 3, 2, 1, 1, 8, 9, 7}
Mean Median: Mode: Range:
(b) Find standard deviation without using calculator for this data set:
{4, -6, 5, -7}
2
22
1
1
x xs
n
n x xs
n n
Problem 4: For the given set of data create a histogram:
{9, 1, 5, 3, 6, 8, 8, 4, 3, 2, 1, 1, 8, 9, 7}. To find class frequencies, find the number of digits in
each class.
Step 1: Find the class boundaries and frequencies
Classes Frequency Class boundaries
1 2 -------------
3 4 -------------
5 6 -------------
7 8 -------------
9 10 -------------
Step 2: Create a histogram for the above dataset
Problem 5: Assume that you take a random sample of 200 people from Salinas and find that
their average income is $48,000 per year with a standard deviation of $9000:
(a) What can you say about the number of people who make between $25,500 and $70,500 out
of the sample of 200 people?
(b) What can you say about the number of people who make more than $70,500 out of the
sample of 200 people?
(c) Now assume that you are given the additional information that the average yearly earning in
Salinas is Bell shaped. Now what can you say about the number of people who make more than
$57,000 per year? Draw graph and label it.
(d) If the data distribution is bell shaped, then approximately how many people make between
$39,000 and $66,000? Draw graph and label it.
Problem 6:A couple wants to have three babies for the next three years, only one baby per year
(either boy or girl) and no other possibility.
Create a sample space, i.e. collection of all simple events:
Find the probability that they will have two girls and a boy.
Find the probability that they will have at least one girl.
Find the probability that they will have no more than two boys.
Find the probability that they will have no girls.
Find the probability that they will have between one and three girls.
Problem 7: Determine whether the following events are independent or dependent:
a) Being African American or any person of color raised in a the poverty stricken part of a big
city and going to college for higher education
b) Growing up in beautiful Pebble beach community and going to college for higher education
c) A randomly selected student from CA community colleges being successful in four year
college and a randomly selected student from MA community colleges being successful in four
year college
Problem 8: Disjoint events?
a) A person being born in the U.S. and the same person being born in Mexico
b) Father having a college degree and the son having a college degree from the same college as
the father did
c) Sunshine and drizzle
Problem 9: Quality Control: As a quality control manager in a clothing company you randomly
select 5 shirts from a collection of 2000 shirts that just came to your company from Bangladesh.
You will reject all the shirts of if you find at least one faulty shirt. It is assumed that there are 20
faulty shirts in the lot of 2000 shirts. Find the probability of accepting all the shirts in this lot.
Problem 10: On the day of an important exam such as the SAT, you keep a backup mechanical
pencil in the event one fails so that you may use the other. Given that there is a 95% chance that
a mechanical pencil would work, what are your chances that you would not have to get a third
mechanical pencil at the test center at the expense of your precious exam time?
Problem 11: Two events A and B are disjoint if P(A and B) = 0. Are the events A and
Bdisjoint? Use the formula P(A or B) = P(A) + P(B) – P(A and B) and find the value of P(A
and B)given thatP(A) = 0.6, P(B) = 0.3, P(A or B) = 0.7
Problem 12:The average income for the city of Salinas is normally distributed with a mean of
$48,000 and a standard deviation of $9,000. Find the z-scores associated with the following
incomes:
Income for Mr. Chris Mickens is $16,000 per year
Income for Ms. Sandra is $90,000 per year
Are the above data outliers? Explain why.
Problem 13:You have the option of buying one car from 5 different types of cars and you may
pick one insurance from 4 different choices. What are total number of ways you can have the car
and insurance combination?
Problem 14:An access code has 6 characters. First four are digits and the last two are alphabets
which are case sensitive. A thief trying to break this code has a probability of success:
Problem 15:A student committee consists of 13 members. They need to elect a president, a vice
president, and a treasurer. How many different ways this can be accomplished?
Problem 16:Age discrimination: Among 13 managers the company laid off 3 oldest managers.
Do you think there was discrimination involved in the process based on your calculations?
Problem 17: Permutation and combination:What are your chances of winning the Mega
Millions Lottery? In Mega Millions you pick 5 numbers from 1 to 56 without replacement and 1
number from 1 to 46.
Problem 18: In a hiring process at a company 6 top managers were hired by taking into
consideration the diversity of pool of applicants drawn from a community which had at least
80% minority populations. At the end of the hiring process no minority manager was hired from
a pool of 30 applicants which proportionately represented the population of the community. Do
you have enough statistical/mathematical justification to question the integrity of the hiring
process given that at least 80% of the population in that community is minority?
END OF MIDTERM 1 REVIEW
Review Problems – Math 13 – Statistics
Name: (Please PRINT)
Problem 1: Identify different levels of measurements for (a) through (d)
(a) Heights of buildings in the city of Salinas
Nominal Ordinal Interval Ratio
(b) Temperature on different days of the year in Salinas
Nominal Ordinal Interval Ratio
(c) Possible letter grades you may receive in the class
Nominal Ordinal Interval Ratio
(d) Names of 10 students from the class
Nominal Ordinal Interval Ratio
(e) Identify different types of sampling and data:
At a buffet they have different types of foods; these are American food, Asian food, Indian food,
and Italian food. You eat two items randomly from each category of food.
Convenience Systematic Stratified Clustering
(f) Determine if the following example represents discrete or continuous data:
Candy store sells candies only in the following amount: 0.2 lbs, 0.4 lbs, 0.6 lbs…
Continuous Discrete
(g) Many students are getting A’s in Mo’s Statistics class. Tom says Mo is a great teacher, while
Jessica says Mo is an easy grader. This situation is called:
Problem 2: Your grade in the class consists of 2 midterms 15% each, homework 10%, project
5%, attendance 10%, and final 30%. Find the weighted mean if your scores are as follows in the
class.
Midterm 1: 85
Midterm 2: 90
Final: 80
Homework: 95
Project: 100
Attendance: 75
Weighted Mean: w x
xw
Problem 3:
(a) Find the following for this data set {9, 1, 5, 3, 6, 8, 8, 4, 3, 2, 1, 1, 8, 9, 7}
Mean Median: Mode: Range:
(b) Find standard deviation without using calculator for this data set:
{4, -6, 5, -7}
2
22
1
1
x xs
n
n x xs
n n
Problem 4: For the given set of data create a histogram:
{9, 1, 5, 3, 6, 8, 8, 4, 3, 2, 1, 1, 8, 9, 7}. To find class frequencies, find the number of digits in
each class.
Step 1: Find the class boundaries and frequencies
Classes Frequency Class boundaries
1 2 -------------
3 4 -------------
5 6 -------------
7 8 -------------
9 10 -------------
Step 2: Create a histogram for the above dataset
Problem 5: Assume that you take a random sample of 200 people from Salinas and find that
their average income is $48,000 per year with a standard deviation of $9000:
(a) What can you say about the number of people who make between $25,500 and $70,500 out
of the sample of 200 people?
(b) What can you say about the number of people who make more than $70,500 out of the
sample of 200 people?
(c) Now assume that you are given the additional information that the average yearly earning in
Salinas is Bell shaped. Now what can you say about the number of people who make more than
$57,000 per year? Draw graph and label it.
(d) If the data distribution is bell shaped, then approximately how many people make between
$39,000 and $66,000? Draw graph and label it.
Problem: A data set has a Bell shape with a mean of 23 and a standard deviation of 4.
(a) Find the data point that is associated with az-score of -1.85.
(b) Is the data point you found in part (a) an outlier? Explain.
Problem 6:A couple wants to have three babies for the next three years, only one baby per year
(either boy or girl) and no other possibility.
Create a sample space, i.e. collection of all simple events:
Find the probability that they will have two girls and a boy.
Find the probability that they will have at least one girl.
Find the probability that they will have no more than two boys.
Find the probability that they will have no girls.
Find the probability that they will have between one and three girls.
Problem 7: Determine whether the following events are independent or dependent:
a) Being African American or any person of color raised in a the poverty stricken part of a big
city and going to college for higher education
b) Growing up in beautiful Pebble beach community and going to college for higher education
c) A randomly selected student from CA community colleges being successful in four year
college and a randomly selected student from MA community colleges being successful in four
year college
Problem 8: Disjoint events?
a) A person being born in the U.S. and the same person being born in Mexico
b) Father having a college degree and the son having a college degree from the same college as
the father did
c) Sunshine and drizzle
Problem 9: Quality Control: As a quality control manager in a clothing company you randomly
select 5 shirts from a collection of 2000 shirts that just came to your company from Bangladesh.
You will reject all the shirts of if you find at least one faulty shirt. It is assumed that there are 20
faulty shirts in the lot of 2000 shirts. Find the probability of accepting all the shirts in this lot.
Problem 10: On the day of an important exam such as the SAT, you keep a backup mechanical
pencil in the event one fails so that you may use the other. Given that there is a 95% chance that
a mechanical pencil would work, what are your chances that you would not have to get a third
mechanical pencil at the test center at the expense of your precious exam time?
Problem 11: Two events A and B are disjoint if P(A and B) = 0. Are the events A and
Bdisjoint? Use the formula P(A or B) = P(A) + P(B) – P(A and B) and find the value of P(A
and B)given thatP(A) = 0.6, P(B) = 0.3, P(A or B) = 0.7
Problem 12:
|
P A and BP B A
P A
In a statistics class the following are the outcomes at the end of the semester:
Passed Failed
Students who expected to pass 35 5
Students who expected to fail 4 15
Find the probability that a randomly selected student passed, given that the student expected to
fail.
Problem 13:You have the option of buying one car from 5 different types of cars and you may
pick one insurance from 4 different choices. What are total number of ways you can have the car
and insurance combination?
Problem 14:An access code has 6 characters. First four are digits and the last two are alphabets
which are case sensitive. A thief trying to break this code has a probability of success:
Problem 15:A student committee consists of 13 members. They need to elect a president, a vice
president, and a treasurer. How many different ways this can be accomplished?
Problem 16:Age discrimination: Among 13 managers the company laid off 3 oldest managers.
Do you think there was discrimination involved in the process based on your calculations?
Problem 17: Permutation and combination:What are your chances of winning the Mega
Millions Lottery? In Mega Millions you pick 5 numbers from 1 to 56 without replacement and 1
number from 1 to 46.
Problem 18: In a hiring process at a company 6 top managers were hired by taking into
consideration the diversity of pool of applicants drawn from a community which had at least
80% minority populations. At the end of the hiring process no minority manager was hired from
a pool of 30 applicants which proportionately represented the population of the community. Do
you have enough statistical/mathematical justification to question the integrity of the hiring
process given that at least 80% of the population in that community is minority?
Problem 19:Assume that you are investing $10,000 in one bond. There are two types of bonds
available. The first bond gives you a 7% return with a default rate of 3% and the second bond
gives you a return of 9% with a default rate of 5%. Which one these bonds would you consider
for investing your $10,000 assuming that you want to maximize your profit.
Problem 20:A new drug named CURAIDS that is 60% effective in extending the average life of
an AIDS patient by twenty years. Five randomly selected AIDS patients from Africa are treated
with this new drug. Answer the following questions based on the above information.
(a) Show that the above situation satisfies all four criteria for the Binomial probability
distribution.
(b) (10 points) Fill in the probabilities in the following table. Show your calculations.
x 0 1 2 3 4 5
P(x)
(c) What is the probability that no more than 4 patients are cured? Use results from part (b), do
not do the calculations again.
(d) Find the probability that more than 2 patients or less than or equal to 5 patients are cured.
Use results from part (b), do not do the calculations again.
(e) Find the probability that at least 4 patients are cured. Use results from part (b), do not do the
calculations again.
(f) Find probability that less than 2 or more than 3 patients are cured. Use results from part (b),
do not do the calculations again.
Problem 21:In a city named Dhaka there were 125 drug related crimes over one year period.
Find the probability that on a given day there will be exactly 3 drug related crimes in that city.
UsePoisson distribution. Explain the requirements for Poisson distribution.
( )!
x eP x
x
Problem 22: Normal approximation to Binomial Distribution: Assume that the probability of giving birth to a baby boy is 0.5; find the probability of giving
birth to at least 180 boys when a survey was conducted on 300 pregnant women. Draw
appropriate graphs and label the points of interest.
Problem 23: Dr. Mohammed Yunus who won the Nobel Peace prize for promoting micro-
financing/mini-loan (normally under $200 per person) for women around the world, especially in
Bangladesh. In a survey of 1000 people who received micro-financing, 89% said that people
who received micro-financing have benefitted from this innovative program. Given that there is
a 50% chance of success for a micro-finance program, find probability that at least 890 people,
i.e. 89% of 1000 people surveyed would say that micro-financing was beneficial.
Problem 24: According to the U.N. report, the average yearly income in Bangladesh is about
$500/year. It is also estimated that the population standard deviation is $100. Find the following
probabilities:
a) If you randomly select a person find the probability that she/he would make between $400 and
$600.
b) If you randomly select 30 persons find the probability that their average yearly income would
be between $400 and $600.
Problem 25: (Normal Distribution)It is known that the average life for a DVD player is 5.4
years and a standard deviation of 0.94 years. If you want to provide a warranty so that only 2%
of the DVD players will be replaced before the warranty expires, what is the time length of the
warranty? Assume normal distribution.
Problem 26: (Normal Distribution)Assume that you are a restaurant owner. The customer
waiting time at your restaurant is normally distributed with an average waiting time of 12
minutes and a standard deviation of 3 minutes. You want to reward (with a free burger) 2% of
the customers who wait the longest amount of time. So what should you tell your customers
about minimum waiting period before they can get a free burger?
Problem 27:Amounts of nicotine in cigarettes (in general) have a mean of 0.952 grams and a
standard deviation of 0.33 grams. The manufacturers claim that they have reduced the amounts
of nicotine in their cigarettes. You do a survey and find that 50 cigarettes have mean nicotine of
0.893 grams. Assume that the mean and the standard deviation of nicotine in cigarettes have not
changed, based on this information find the probability of randomly selecting 50 cigarettes with
a mean of 0.893 or less. Also based on your calculations, would you agree with the
manufacturer’s claim?
Problem 28: In a survey of 200 Hartnell students, it was found that 60 students said that English
was not their first language. Create a 95% confidence interval for true proportion of Hartnell
students whose first language is not English.
Assumptions:
Margin of error:
Graph:
Confidence interval:
Explanation of confidence interval:
Problem 29: Population proportion A Popular TV show named ROOTS that addressed the
black history and culture in the U.S. was very popular in the 1980s. You are curious if the
majority of the population nowadays have heard of this show or know about it. Your research
indicated that 241 people knew about this show out of 495 people you surveyed. Create a 95%
confidence interval for the true population proportion.
Assumptions:
Graph:
Margin of error:
Confidence interval and explanation:
Problem 30: t-distribution: Following table represents the number of hours 10 different
Hartnell College students work per week.
20 35 23 25 38 15 41 33 19 29
It is known that the distribution of the number of hours a HartnellCollege student works has
approximately bell shape. Create a 95% confidence interval for the true mean of the number of
hours per week a HartnellCollege student works.
Assumptions:
Calculations: / 2
x E x E
sE t
n
Graphs:
Confidence interval and explanation:
Problem 31: Assume that the distribution of average yearly salary for Hartnell College
graduates is a bell shaped curve. A random sample of 13 Hartnell College graduates has a mean
salary of $35,000 and a standard deviation of $5,000. Create a 95% confidence interval for the
population standard deviation.
Assumptions:
Calculations: 2 2
2
2 2
1 1
R L
n s n s
Graph:
Confidence interval and explanation:
Problem 32:It is known that in Bangladesh a person makes on the average $75 a month with a
standard deviation of $9. You, as a researcher, are interested in determining if the monthly
average income per person has increased. Therefore, you take a random sample of 100 people
and find that the sample average is $79. If you desire a significance level of 0.05, then state your
conclusion based on the calculations you make.
Assumptions:
Null and Alternative hypotheses:
Calculations: x
z
n
Graph and critical values:
P-value:
Conclusions:
Problem 33:A Popular TV show named ROOTS that addressed the black history and culture in
the U.S. was very popular in the 1980s. You are curious if the majority (more than 50%) of the
population nowadays have heard of this show or know about it. Your research indicated that 241
people knew about this show out of 495 people you surveyed. What is your conclusion?
Significance level is 0.05.
Assumptions:
Null and Alternative hypotheses:
Calculations:p̂ p
zpq
n
Graph and critical values:
P-value:
Conclusion:
Problem 34:Hypothesis Testing: 200 field workers were surveyed and their average yearly
income was $13,700. The population standard deviation for the income distribution of field
workers is assumed to be $4,000. Use the sample data, with 0.05 significance level, and test the
claim that average income for the population of field workers is different from $14,000 per year.
Requirements:
Null and Alternative Hypotheses:
Test Statistic: * xxz
n
Graph and critical regions:
P-value:
Conclusion:
Problem 35:Hypothesis test: (Matched pair) An exercise program is claimed to be effective in
reducing weight. The following represents the weights of 8 people before and after the exercise
program. Is there sufficient evidence to support the claim that there is a difference in weights
before and after the program? Use a 0.05 significance level.
Before 150 135 191 210 189 123 132 175
After 148 136 172 192 185 120 135 170
Assumptions:
Null and alternative hypotheses:
Calculations:
* ddt
s
n
and degrees of freedom = n – 1
Graphs and critical points:
Conclusion:
Problem 36: Two population proportions inferences: According to the PEW Research Center for
the People & the Press in 2000 approximately 50% of the people surveyed said that the
immigrants strengthen the U.S. with their hard work and talents whereas in 2006 approximately
41% responded similarly. Let us assume that each year the survey was conducted on 2,000
randomly selected adults in the U.S. Based on this information would you conclude that there is
a progressively negative attitude towards immigrants in the U.S.? (Use significance level of 0.05,
i.e. 95% confidence level)
Assumptions:
Null and alternative hypotheses:
Calculations:
1 2 1 2*
1 2
1 2 1 21 2
1 2 1 2
ˆ ˆTest Statistic:
ˆ ˆwhere and and and 1
p p p pz
pq pq
n n
x x x xp p p q p
n n n n
Graphs and critical points:
Conclusion:
Create a confidence interval:
1 2 1 2 1 2
1 1 2 2/2
1 2
ˆ ˆ ˆ ˆ
ˆ ˆ ˆ ˆwhere margin of error:
p p E p p p p E
p q p qE z
n n
Problem 37: A 50-year long study by the British researchers shows that on the average smokers
live 10 years less than the nonsmokers do. You being the curious cat collected some data from a
reliable source and found that 621 smokers had average life span of 77 while 831 nonsmokers
had an average life of 71. You also have the information that the sample standard deviation for
life expectancy for both the smokers and nonsmokers is 10. Based on this information would
you reject the null hypothesis that there is no difference in the average life expectancy between
the smokers and nonsmokers?
Assumptions:
Null and alternative hypotheses:
Calculations:
1 2 1 2*
2 2
1 2
1 2
Test Statistic: x x
ts s
n n
Graphs and critical points:
Conclusion:
Problem 38: F-distribution: A new drug was tested on treatment population and placebo
population. Test the claim that variances for two populations differ. Significance level is 0.05.
Treatment group: sample size = 17, mean = 23.84, standard deviation = 2.31
Placebo group: sample size = 36, mean = 21.97, standard deviation = 2.01
Assumptions:
Null and alternative hypotheses:
Calculations: 2
* 1
2
2
Test Statistic: s
Fs
Graph and critical values:
Conclusion:
Problem 39: Following represents the amount of tips paid for different bills at a restaurant.
Bill (in $) 20 15 39 69 55 72 85 79
Tips (in $) 5 5 8 10 15 10 20 15
(a) Use hypothesis testing to determine whether there is linear correlation between the bill and
the tip paid?
*
21
2
rt
r
n
Degree of freedom (n – 2)
(b) Find the equation of the regression line for the above set of data.
(c) Predict tip for $95.
(d) Predict tip for $72
Problem 40:ANOVA: Use F-distribution
Given below are electricity consumptions for four different cities for five different months. Use
a 0.05 significance level to test the null hypothesis that different cities have the same mean for
electricity consumption.
Jan. May July Oct. Nov
City A: 25 29 41 35 36
City B: 30 24 26 39 34
City C: 41 22 28 41 44
City D: 36 31 43 40 35
Assumptions:
Null and Alternative hypotheses:
Calculations:
Graphs:
Conclusions: