Question 1

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.

Accepted Answer

The answer of The International Olympic Committee states that the...

Question 2

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.

Accepted Answer

The answer of A report on health care in the...

Question 3

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?

Accepted Answer

The answer of Approval rating A newspaper article reported that...

Question 4

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.

Accepted Answer

The answer of A company manufacturing computer chips finds that...

Question 5

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.

Accepted Answer

The answer of A company manufacturing computer chips finds that...

Question 6

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.

Accepted Answer

The answer of Graduation tests Many states mandate tests that...

Question 7

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.

Accepted Answer

The answer of Herpetologists (snake specialists) found that a certain...

Question 8

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.

Accepted Answer

The answer of A state's Department of Education reports that...

Question 9

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.

Accepted Answer

The answer of Approval rating The President's job approval rating...

Question 10

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.

Accepted Answer

The answer of According to the 2010 census, 20.3% of...

Question 11

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?

Accepted Answer

The answer of Pumpkin pie A can of pumpkin pie...

Question 12

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: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | l | } 
\hline 12 & 13 & 14 & 14 & 15 & 15 & 15 & 16 & 16 & 16 & 16 & 16 \
\hline 17 & 17 & 17 & 18 & 18 & 18 & 18 & 19 & 19 & 19 & 20 & 21 \
\hline
\end{array}$$
-Does this sample indicate that students are taking more credit hours than the professor
believes? Test an appropriate hypothesis and state your conclusion.

Accepted Answer

The answer of A professor at a large university believes...

Question 13

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.

Accepted Answer

The answer of According to the 2010 census, 20.3% of...

Question 14

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.)

Accepted Answer

The answer of A report on health care in the...

Question 15

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?

Accepted Answer

The answer of A statistics professor asked her students whether...

Question 16

Explain what your P-value means in this context.

Accepted Answer

The answer of Explain what your P-value means in this...

Question 17

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.

Accepted Answer

The answer of Depression A recent psychiatric study from the...

Question 18

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?

Accepted Answer

The answer of Egg weights The weights of hens' eggs...

Question 19

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.

Accepted Answer

The answer of The countries of Europe report that 46%...

Question 20

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?

Accepted Answer

The answer of The owner of a small clothing store...

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

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?

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?

Explain what your P-value means in this context.

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?