Deck 5: From the Data at Hand to the World at Large

Question 1

A certain population is strongly skewed to the right. We want to estimate its mean, so we will
Collect a sample. Which should be true if we use a large sample rather than a small one?
I) The distribution of our sample data will be closer to normal.
II) The sampling model of the sample means will be closer to normal.
III) The variability of the sample means will be greater.

A) I only
B) II and III only
C) III only
D) II only
E) I and III only

Answer 1

D

Question 2

We have calculated a confidence interval based upon a sample of . Now we want to get a
Better estimate with a margin of error only one fifth as large. We need a new sample with n at least
…

A) 240
B) 1000
C) 5000
D) 450
E) 40

Answer 2

C

Question 3

Answer 3

A

Question 4

We have calculated a 95% confidence interval and would prefer for our next confidence interval to
Have a smaller margin of error without losing any confidence. In order to do this, we can
I) change the
Value to a smaller number.
II) take a larger sample.
III) take a smaller sample.

A) I and II
B) II only
C) III only
D) I only
E) I and III

Question 5

Which is true about a 98% confidence interval for a population proportion based on a given
Sample?
I) We are 98% confident that other sample proportions will be in our interval.
II) There is a 98% chance that our interval contains the population proportion.
III) The interval is wider than a 95% confidence interval would be.

A) III only
B) I and II
C) I only
D) II only
E) none of these

Question 6

A certain population is strongly skewed to the left. We want to estimate its mean, so we collect a
Sample. Which should be true if we use a large sample rather than a small one?
I) The distribution of our sample data will be more clearly skewed to the left.
II) The sampling model of the sample means will be more skewed to the left.
III) The variability of the sample means will greater.

A) II and III only
B) III only
C) II only
D) I and III only
E) I only

Question 7

The manager of an orchard expects about 70% of his apples to exceed the weight requirement for
"Grade A" designation. At least how many apples must he sample to be 90% confident of
Estimating the true proportion within ±4%?

A) 89
B) 505
C) 19
D) 23
E) 356

Question 8

Suppose that a conveyor used to sort packages by size does not work properly. We test the
Conveyor on several packages (with
Nd our data results in a P-value of 0.016.
What probably happens as a result of our testing?

Question 9

We are about to test a hypothesis using data from a well-designed study. Which is true?
I) A small P-value would be strong evidence against the null hypothesis.
II) We can set a higher standard of proof by choosing
III) If we reduce the alpha level, we reduce the power of the test.

A) none of these
B) I only
C) III only
D) II only
E) I and III only

Question 10

We have calculated a confidence interval based on a sample of . Now we want to get a better
Estimate with a margin of error only one third as large. We need a new sample with n at least…

A) 312
B) 1620
C) 60
D) 540
E) 20

Question 11

A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10
Squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32
Grams and standard deviation of 1.88gm. Assuming these squirrels can be considered a random
Sample of all red squirrels which of the following formulas gives a 95% confidence interval for the
Mean weight of all squirrels?

Question 12

Suppose that a device advertised to increase a car's gas mileage really does not work. We test it on a
Small fleet of cars (with H0: not effective), and our data results in a P-value of 0.004. What
Probably happens as a result of our experiment?

Question 13

Not wanting to risk poor sales for a new soda flavor, a company decides to run one more taste test
On potential customers, this time requiring a higher approval rating than they had for earlier tests.
This higher standard of proof will increase
I) the risk of Type I error
II) the risk of Type II error
III) power

A) II only
B) III only
C) I only
D) I and III
E) I and II

Question 14

An online catalog company wants on-time delivery for at least 90% of the orders they ship. They
Have been shipping orders via UPS and FedEx but will switch to a more expensive service
(ShipFast) if there is evidence that this service can exceed the 90% on-time goal. As a test the
Company sends a random sample of orders via ShipFast, and then makes follow-up phone calls to
See if these orders arrived on time. Which hypotheses should they test?

Question 15

Which is true about a 95% confidence interval based on a given sample?
I) The interval contains 95% of the population.
II) Results from 95% of all samples will lie in the interval.
III) The interval is narrower than a 98% confidence interval would be.

A) II and III only
B) II only
C) none of these
D) III only
E) I only

Question 16

We have calculated a confidence interval based on a sample of size Now we want to get a
Better estimate with a margin of error that is only one-fourth as large. How large does our new
Sample need to be?

A) 1600
B) 25
C) 400
D) 50
E) 200

Question 17

A) No, because they only used a sample of the applicants instead of all of them.
B) No, because financial aid amounts may not be normally distributed.
C) Yes; since 35% is in the confidence interval they accept the null hypothesis, concluding that the percentage of students requiring financial aid will stay the same.
D) Yes; since 35% is in the confidence interval they fail to reject the null hypothesis, concluding that there is not strong evidence of any change in financial aid requests.
E) Yes; since 35% is not at the center of the confidence interval they reject the null hypothesis, concluding that the percentage of students requiring aid will increase.

Question 18

A P-value indicates

A) the probability that the null hypothesis is true.
B) the probability that the alternative hypothesis is true.
C) the probability of the observed statistic given that the null hypothesis is true.
D) the probability of the observed statistic given that the alternative hypothesis is true.
E) the probability the null is true given the observed statistic.

Question 19

We are about to test a hypothesis using data from a well-designed study. Which is true?
I) A large P-value would be strong evidence against the null hypothesis.
II) We can set a higher standard of proof by choosing
III) If we reduce the risk of committing a Type I error, then the risk of a Type II error will also
Decrease.

A) none of these
B) III only
C) II only
D) I only
E) I and II only

Question 20

A certain population is bimodal. We want to estimate its mean, so we will collect a sample. Which
Should be true if we use a large sample rather than a small one?
I) The distribution of our sample data will be more clearly bimodal.
II) The sampling distribution of the sample means will be approximately normal.
III) The variability of the sample means will be smaller.

A) I, II, and III
B) III only
C) II and III
D) I only
E) II only

Question 21

Which is true about a 99% confidence interval based on a given sample?
I) The interval contains 99% of the population.
II) Results from 99% of all samples will lie in this interval.
III) The interval is wider than a 95% confidence interval would be.

A) II only
B) I only
C) II and III only
D) none of these
E) III only

Question 22

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. The
insurance company knows that, last year, the life expectancy of its policyholders was 77 years. They want to know if their
clients this year have a longer life expectancy, on average, so the company randomly samples some of the recently paid
policies to see if the mean life expectancy of policyholders has increased. The insurance company will only change their
premium structure if there is evidence that people who buy their policies are living longer than before.
For more accurate cost determination, the insurance companies want to estimate the life
expectancy to within one year with 95% confidence. How many randomly selected records
would they need to have?

Question 23

A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the
End of the term, she takes a random sample of students from her large class and asks, in an
Anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she
Test?

Question 24

Wildlife scientists studying a certain species of frogs know that past records indicate the
adults should weigh an average of 118 grams with a standard deviation of 14 grams. The
researchers collect a random sample of 50 adult frogs and weigh them. In their sample the
mean weight was only 110 grams. One of the scientists is alarmed, fearing that
environmental changes may be adversely affecting the frogs. Do you think this sample
result is unusually low? Explain.

Question 25

A researcher investigating whether joggers are less likely to get colds than people who do not jog
Found a P-value of 3%. This means that:

A) 3% of joggers get colds.
B) There's a 3% chance that joggers don't get fewer colds.
C) none of these
D) Joggers get 3% fewer colds than non-joggers.
E) There's a 3% chance that joggers get fewer colds.

Question 26

A company claims to have invented a hand-held sensor that can detect the presence of explosives inside a closed container.
Law enforcement and security agencies are very interested in purchasing several of the devices if they are shown to perform
effectively. An independent laboratory arranged a preliminary test. If the device can detect explosives at a rate greater than
chance would predict, a more rigorous test will be performed. They placed four empty boxes in the corners of an otherwise
empty room. For each trial they put a small quantity of an explosive in one of the boxes selected at random. The company's
technician then entered the room and used the sensor to try to determine which of the four boxes contained the explosive.
The experiment consisted of 50 trials, and the technician was successful in finding the explosive 16 times. Does this indicate
that the device is effective in sensing the presence of explosives, and should undergo more rigorous testing?
Test an appropriate hypothesis and state your conclusion.

Question 27

The owner of a small clothing store is concerned that only 28% of people who enter her store actually buy something. A
marketing salesman suggests that she invest in a new line of celebrity mannequins (think Seth Rogan modeling the latest
jeans…). He loans her several different "people" to scatter around the store for a two-week trial period. The owner carefully
counts how many shoppers enter the store and how many buy something so that at the end of the trial she can decide if she'll
purchase the mannequins. She'll buy the mannequins if there is evidence that the percentage of people that buy something
increases.
Over the trial month the rate of in-store sales rose to 30% of shoppers. The store's owner
decided this increase was statistically significant. Now that she's convinced the
mannequins work, why might she still choose not to purchase them?

Question 28

The average composite ACT score for Ohio students who took the test in 2003 was 21.4.Assume that the standard deviation is 1.05. In a random sample of 25 students who took
the exam in 2003, what is the probability that the average composite ACT score is 22 or
more? (Make sure to identify the sampling distribution you use and check all necessary
conditions.)

Question 29

A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned
that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective
chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive
program is instituted for one month. If successful, the company will continue with the incentive program.
In this context describe a Type II error and the impact such an error would have on the
company.

Question 30

The owner of a small clothing store is concerned that only 28% of people who enter her store actually buy something. A
marketing salesman suggests that she invest in a new line of celebrity mannequins (think Seth Rogan modeling the latest
jeans…). He loans her several different "people" to scatter around the store for a two-week trial period. The owner carefully
counts how many shoppers enter the store and how many buy something so that at the end of the trial she can decide if she'll
purchase the mannequins. She'll buy the mannequins if there is evidence that the percentage of people that buy something
increases.
In this context describe a Type II error and the impact such an error would have on the
store.

Question 31

A pharmaceutical company investigating whether drug stores are less likely than food markets to
Remove over-the-counter drugs from the shelves when the drugs are past the expiration date
Found a P-value of 2.8%. This means that:

A) none of these
B) There is a 2.8% chance the drug stores remove more expired over-the-counter drugs.
C) There is a 97.2% chance the drug stores remove more expired over-the-counter drugs.
D) 2.8% more drug stores remove over-the-counter drugs from the shelves when the drugs are past the expiration date.
E) 97.2% more drug stores remove over-the-counter drugs from the shelves when the drugs are past the expiration date than drug stores.

Question 32

A coffee house owner knows that customers pour different amounts of coffee into their cups. She
Samples cups from 10 costumers she believes to be representative of the customers and weighs the
Cups, finding a mean of 12.5 ounces and standard deviation of 0.5 ounces. Assuming these cups of
Coffee can be considered a random sample of all cups of coffee which of the following formulas
Gives a 95% confidence interval for the mean weight of all cups of coffee?

Question 33

Which of the following is true about Type I and Type II errors?
I) Type I errors are always worse than Type II errors.
II) The severity of Type I and Type II errors depends on the situation being tested.
III) In any given situation, the higher the risk of Type I error, the lower the risk of Type II error.

A) III only
B) II only
C) I and III
D) I only
E) II and III

Question 34

Question 35

To plan the course offerings for the next year a university department dean needs to estimate what
Impact the "No Child Left Behind" legislation might have on the teacher credentialing program.
Historically, 40% of this university's pre-service teachers have qualified for paid internship
Positions each year. The Dean of Education looks at a random sample of internship applications to
See what proportion indicate the applicant has achieved the content-mastery that is required for
The internship. Based on these data he creates a 90% confidence interval of (33%, 41%). Could this
Confidence interval be
Used to test the hypothesis
0)05 level of significance?

A) No, because the dean only reviewed a sample of the applicants instead of all of them.
B) No, because he should have used a 95% confidence interval.
C) Yes, since 40% is not the center of the confidence interval he rejects the null hypothesis, concluding that the percentage of qualified applicants will decrease.
D) Yes, since 40% is in the confidence interval he accepts the null hypothesis, concluding that the percentage of applicants qualified for paid internship positions will stay the same.
E) Yes, since 40% is in the confidence interval he fails to reject the null hypothesis, concluding that there is not strong enough evidence of any change in the percent of qualified applicants.

Question 36

Question 37

The board of directors for Procter and Gamble is concerned that only 19.5% of the people who use toothpaste buy Crest
toothpaste. A marketing director suggests that the company invest in a new marketing campaign which will include
advertisements and new labeling for the toothpaste. The research department conducts product trials in test markets for one
month to determine if the market share increases with new labels.
Based on the data they collected during the trial the research department found that a 98%
confidence interval for the proportion of all consumers who might buy Crest toothpaste
was (16%, 28%). What conclusion should the company reach about the new marketing
campaign? Explain.

Question 38

Pew Research reports that 63% of the U.S. adult cell phone owners use their phone to go online. A company wants to target
16- to 24-year olds for advertising and they wonder if that age group has a similar pattern of phone use.
They ignore your advice in Question 1 and just select a random sample of 300 cell phone
users aged 16 to 24, and find that 206 of those surveyed use their phone to go online. Create
the confidence interval.

Question 39

Question 40

According to the 2010 census, 20.3% of the population of the United States (ages 5 and up) live in a home in which a language
other than English is spoken. Advocates for providing government programs to assist non-English speakers are convinced
that, with the increasing non-white population in the United States, this proportion has probably increased. They plan to
conduct a survey, and if they find the proportion of people who live in such homes has increased, they will organize a
campaign to increase government investment in these assistance programs.
In this context describe a Type I error and the impact such an error would have on this
group's efforts.

Question 41

The International Olympic Committee states that the female participation in the 2004 Summer Olympic Games was 42%,
even with new sports such as weight lifting, hammer throw, and modern pentathlon being added to the Games. Broadcasting
and clothing companies want to change their advertising and marketing strategies if the female participation increases at the
next games. An independent sports expert arranged for a random sample of pre-Olympic exhibitions. The sports expert
reported that 202 of 454 athletes in the random sample were women. Is this strong evidence that the participation rate may
increase?
Explain what your P-value means in this context.

Question 42

A report on health care in the US said that 28% of Americans have experienced times when they haven't been able to afford
medical care. A news organization randomly sampled 801 black Americans, of whom 38% reported that there had been times
in the last year when they had not been able to afford medical care. Does this indicate that this problem is more severe among
black Americans?
Was your test one-tail upper tail, one-tail lower tail, or two-tail? Explain why you chose
that kind of test in this situation.

Question 43

Approval rating A newspaper article reported that a poll based on a sample of 1150
residents of a state showed that the state's Governor's job approval rating stood at 58%.
They claimed a margin of error of ±3%. What level of confidence were the pollsters using?

Question 44

A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned
that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective
chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive
program is instituted for one month. If successful, the company will continue with the incentive program.
Write the company's null and alternative hypotheses.

Question 45

A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned
that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective
chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive
program is instituted for one month. If successful, the company will continue with the incentive program.
In this context describe a Type I error and the impact such an error would have on the
company.

Question 46

Graduation tests Many states mandate tests that have to be passed in order for students to
graduate with a high school diploma. A local school superintendent believes that
after-school tutoring will improve the scores of students in his district on the state's
graduation test. A tutor agrees to work with 15 students for a month before the
superintendent will approach the school board about implementing an after-school
tutoring program. The after-school tutoring program will be implemented if student
scores increase by more than 20 points. The superintendent will test a hypothesis using α =
0.02 .
a. Write appropriate hypotheses (in words and in symbols).
b. In this context, which do you consider to be more serious - a Type I or a Type II error?
Explain.
c. After this trial produced inconclusive results, the superintendent decided to test the
after-school tutoring program again with another group of students. Describe two changes
he could make in the trial to increase the power of the test, and explain the disadvantages
of each.

Question 47

Herpetologists (snake specialists) found that a certain species of reticulated python have an
average length of 20.5 feet with a standard deviation of 2.3 feet. The scientists collect a
random sample of 30 adult pythons and measure their lengths. In their sample the mean
length was 19.5 feet long. One of the herpetologists fears that pollution might be affecting
the natural growth of the pythons. Do you think this sample result is unusually small?
Explain.

Question 48

A state's Department of Education reports that 12% of the high school students in that state attend private high schools. The
State University wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random
sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend
private schools.
Explain what 90% confidence means in this context.

Question 49

Approval rating The President's job approval rating is always a hot topic. Your local paper
conducts a poll of 100 randomly selected adults to determine the President's job approval
rating. A CNN/USA Today/Gallup poll conducts a poll of 1010 randomly selected adults.
Which poll is more likely to report that the President's approval rating is below 50%, assuming that his actual approval rating is 54%? Explain.

Question 50

According to the 2010 census, 20.3% of the population of the United States (ages 5 and up) live in a home in which a language
other than English is spoken. Advocates for providing government programs to assist non-English speakers are convinced
that, with the increasing non-white population in the United States, this proportion has probably increased. They plan to
conduct a survey, and if they find the proportion of people who live in such homes has increased, they will organize a
campaign to increase government investment in these assistance programs.
Based on data that were collected during the survey, the advocate group found that a 99%
confidence interval for the proportion of all U.S. residents who live in a home in which a
language other than English is spoken (19.8%, 25.2%). What conclusion should they reach
about the population? Explain.

Question 51

Pumpkin pie A can of pumpkin pie mix contains a mean of 30 ounces and a standard
deviation of 2 ounces. The contents of the cans are normally distributed. What is the
probability that four randomly selected cans of pumpkin pie mix contain a total of more
than 126 ounces?

Question 52

A professor at a large university believes that students take an average of 15 credit hours per term. A random sample of 24
students in her class of 250 students reported the following number of credit hours that they were taking:
Does this sample indicate that students are taking more credit hours than the professor
believes? Test an appropriate hypothesis and state your conclusion.

Question 53

According to the 2010 census, 20.3% of the population of the United States (ages 5 and up) live in a home in which a language
other than English is spoken. Advocates for providing government programs to assist non-English speakers are convinced
that, with the increasing non-white population in the United States, this proportion has probably increased. They plan to
conduct a survey, and if they find the proportion of people who live in such homes has increased, they will organize a
campaign to increase government investment in these assistance programs.
In this context describe a Type II error and the impact such an error would have on this
group's efforts.

Question 54

A report on health care in the US said that 28% of Americans have experienced times when they haven't been able to afford
medical care. A news organization randomly sampled 801 black Americans, of whom 38% reported that there had been times
in the last year when they had not been able to afford medical care. Does this indicate that this problem is more severe among
black Americans?
Test an appropriate hypothesis and state your conclusion. (Make sure to check any
necessary conditions and to state a conclusion in the context of the problem.)

Question 55

A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students
(randomly sampled from her 700 students), 35 said they were registered to vote.
What is the probability that the true proportion of the professor's students who were
registered to vote is in your confidence interval?

Question 56

Explain what your P-value means in this context.

Question 57

Depression A recent psychiatric study from the University of Southampton observed a
higher incidence of depression among women whose birth weight was less than 6.6
pounds than in women whose birth weight was over 6.6 pounds. Based on a P-value of
0.0248 the researchers concluded there was evidence that low birth weights may be a risk
factor for susceptibility to depression. Explain in context what the reported P-value means.

Question 58

Egg weights The weights of hens' eggs are normally distributed with a mean of 56 grams
and a standard deviation of 4.8 grams. What is the probability that a dozen randomly
selected eggs weighs over 690 grams?

Question 59

The countries of Europe report that 46% of the labor force is female. The United Nations wonders if the percentage of females
in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check
a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor
force.
Interpret the confidence interval in this context.

Question 60

The owner of a small clothing store is concerned that only 28% of people who enter her store actually buy something. A
marketing salesman suggests that she invest in a new line of celebrity mannequins (think Seth Rogan modeling the latest
jeans…). He loans her several different "people" to scatter around the store for a two-week trial period. The owner carefully
counts how many shoppers enter the store and how many buy something so that at the end of the trial she can decide if she'll
purchase the mannequins. She'll buy the mannequins if there is evidence that the percentage of people that buy something
increases.
The owner talked the salesman into extending the trial period so that she can base her
decision on data for a full month. Will the power of the test increase, decrease, or remain
the same?

Question 61

The board of directors for Procter and Gamble is concerned that only 19.5% of the people who use toothpaste buy Crest
toothpaste. A marketing director suggests that the company invest in a new marketing campaign which will include
advertisements and new labeling for the toothpaste. The research department conducts product trials in test markets for one
month to determine if the market share increases with new labels.
In this context describe a Type I error and the impact such an error would have on the
company.

Question 62

Textbook authors must be careful that the reading level of their book is appropriate for the target audience. Some methods of
assessing reading level require estimating the average word length. We've randomly chosen 20 words from a randomly
selected page in Stats: Data and Models and counted the number of letters in each word:
5, 5, 2, 11, 1, 5, 3, 8, 5, 4, 7, 2, 9, 4, 8, 10, 4, 5, 6, 6
For a more definitive evaluation of reading level the editor wants to estimate the text's
mean word length to within 0.5 letters with 98% confidence. How many randomly selected
words does she need to use?

Question 63

A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned
that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective
chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive
program is instituted for one month. If successful, the company will continue with the incentive program.
Management decided to extend the incentive program so that the decision can be made on
three months of data instead. Will the power increase, decrease, or remain the same?

Question 64

Too much TV? A father is concerned that his teenage son is watching too much television
each day, since his son watches an average of 2 hours per day. His son says that his TV
habits are no different than those of his friends. Since this father has taken a stats class, he
knows that he can actually test to see whether or not his son is watching more TV than his
peers. The father collects a random sample of television watching times from boys at his
son's high school and gets the following data:
1.9 2.3 2.2 1.9 1.6 2.6 1.4 2.0 2.0 2.2
Is the father right? That is, is there evidence that other boys average less than 2 hours of
television per day? Conduct a hypothesis test, making sure to state your conclusions in the
context of the problem.

Question 65

All 423 Wisconsin public schools were all given a rating by the Wisconsin Department of
Public Instruction based on several variables. The mean rating reported was 71.5 and the
standard deviation was 4.87. To do a follow-up study a random sample of 40 schools was
selected. In this sample, the mean rating was 70.9. One of the researchers is alarmed,
thinking the report may have been mistaken. Do you think this sample result is unusually
low? Explain.

Question 66

The countries of Europe report that 46% of the labor force is female. The United Nations wonders if the percentage of females
in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check
a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor
force.
The representatives from the Department of Labor want to estimate a percentage of
females in the United States labor force to within ±5%, with 90% confidence. How many
employment records should they sample?

Question 67

Cereal A box of Raspberry Crunch cereal contains a mean of 13 ounces with a standard
deviation of 0.5 ounce. The distribution of the contents of cereal boxes is approximately
Normal. What is the probability that a case of 12 cereal boxes contains a total of more than
160 ounces?

Question 68

According to the 2010 census, 20.3% of the population of the United States (ages 5 and up) live in a home in which a language
other than English is spoken. Advocates for providing government programs to assist non-English speakers are convinced
that, with the increasing non-white population in the United States, this proportion has probably increased. They plan to
conduct a survey, and if they find the proportion of people who live in such homes has increased, they will organize a
campaign to increase government investment in these assistance programs.
Describe to the group an advantage and a disadvantage of using an alpha level of 5%
instead.

Question 69

The countries of Europe report that 46% of the labor force is female. The United Nations wonders if the percentage of females
in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check
a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor
force.
Should the representatives from the Department of Labor conclude that the percentage of
females in their labor force is lower than Europe's rate of 46%? Explain.

Question 70

The countries of Europe report that 46% of the labor force is female. The United Nations wonders if the percentage of females
in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check
a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor
force.
Explain what 90% confidence means in this context.

Question 71

A professor at a large university believes that students take an average of 15 credit hours per term. A random sample of 24
students in her class of 250 students reported the following number of credit hours that they were taking:
Find a 95% confidence interval for the number of credit hours taken by the students in the
professor's class. Interpret your interval.

Question 72

15. Baldness and heart attacks A recent medical study observed a higher frequency of
heart attacks among a group of bald men than among another group of men who were not
bald. Based on a P-value of 0.062 the researchers concluded there was some evidence that
male baldness may be a risk factor for predicting heart attacks. Explain in this context what
their P-value means.

Question 73

Pew Research reports that 63% of the U.S. adult cell phone owners use their phone to go online. A company wants to target
16- to 24-year olds for advertising and they wonder if that age group has a similar pattern of phone use.
Interpret the confidence interval in this context.

Question 74

It is generally believed that nearsightedness affects about 12% of children. A school district
gives vision tests to 133 incoming kindergarten children.
a. Describe the sampling distribution model for the sample proportion by naming the
model and telling its mean and standard deviation. Justify your answer.
b. Sketch and clearly label the model.
c. What is the probability that in this group over 15% of the children will be found to be
nearsighted?

Question 75

According to Gallup, about 33% of Americans polled said they frequently experience stress
in their daily lives. Suppose you are in a class of 45 students.
a. What is the probability that no more than 12 students in the class will say that they
frequently experience stress in their daily lives? (Make sure to identify the sampling
distribution you use and check all necessary conditions.)
b. If 20 students in the class said they frequently experience stress in their daily lives,
would you be surprised? Explain, and use statistics to support your answer.

Question 76

The International Olympic Committee states that the female participation in the 2004 Summer Olympic Games was 42%,
even with new sports such as weight lifting, hammer throw, and modern pentathlon being added to the Games. Broadcasting
and clothing companies want to change their advertising and marketing strategies if the female participation increases at the
next games. An independent sports expert arranged for a random sample of pre-Olympic exhibitions. The sports expert
reported that 202 of 454 athletes in the random sample were women. Is this strong evidence that the participation rate may
increase?
Was your test one-tail upper tail, lower tail, or two-tail? Explain why you choose that kind
of test in this situation.

Question 77

According to the 2010 U.S. Census, 11.7% of the people in the state of Oregon were Hispanic or Latino. A political party
wants to know how much impact the Hispanic and Latino vote will have, so they wonder if that percentage has changed
since then. They take a random sample of 853 adults in Oregon and ask, among other things, their race. 113 of the people
surveyed were Hispanic or Latino. Can the political party conclude that the Hispanic proportion of the population has
changed since 2010?
Test an appropriate hypothesis and state your conclusion.

Question 78

The board of directors for Procter and Gamble is concerned that only 19.5% of the people who use toothpaste buy Crest
toothpaste. A marketing director suggests that the company invest in a new marketing campaign which will include
advertisements and new labeling for the toothpaste. The research department conducts product trials in test markets for one
month to determine if the market share increases with new labels.
In this context describe a Type II error and the impact such an error would have on the
company.

Question 79

A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned
that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective
chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive
program is instituted for one month. If successful, the company will continue with the incentive program.
Describe to management an advantage and disadvantage of using a 1% alpha level of
significance instead.

Question 80

The board of directors for Procter and Gamble is concerned that only 19.5% of the people who use toothpaste buy Crest
toothpaste. A marketing director suggests that the company invest in a new marketing campaign which will include
advertisements and new labeling for the toothpaste. The research department conducts product trials in test markets for one
month to determine if the market share increases with new labels.
Describe to the board of directors an advantage and a disadvantage of using a 5% alpha
level of significance instead.