Question 1

A P-value indicates

Accepted Answer

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 2

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.

Accepted Answer

The answer of The board of directors for Procter and...

Question 3

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.
-What alpha level did the store's owner use?

Accepted Answer

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

Question 4

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.
-A consultant talked the group into gathering a larger sample. Will the power of the test
increase, decrease, or remain the same?

Accepted Answer

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

Question 5

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.

Accepted Answer

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

Question 6

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.

Accepted Answer

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

Question 7

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.

Accepted Answer

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

Question 8

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.

Accepted Answer

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

Question 9

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?

Accepted Answer

The answer of Cereal A box of Raspberry Crunch cereal...

Question 10

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.

Accepted Answer

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

Question 11

Roadblocks From time to time police set up roadblocks to check cars to see if the safety
inspection is up to date. At one such roadblock they issued tickets for expired inspection
stickers to 22 of 628 cars they stopped.
a. Based on the results at this roadblock, construct and interpret a 95% confidence interval
for the proportion of autos in that region whose safety inspections have expired.
b. Explain the meaning of "95% confidence" in part a).

Accepted Answer

The answer of Roadblocks From time to time police set...

Question 12

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?
-Was your test one-tail upper tail, lower tail, or two-tail? Explain why you chose that kind
of test in this situation.

Accepted Answer

The answer of A company claims to have invented a...

Question 13

Housing costs A government report on housing costs says that single-family home prices
nationwide are skewed to the right, with a mean of $235,700. We want to see how home
prices in Orange County, California compare with those nationwide.
a. We collect price data from a random sample of 50 homes in Orange County, California.
Why is it okay to use these data for inference even though the population is skewed?
b. The standard deviation of the 50 homes in our sample was $25,500. Specify the sampling
model for the mean price of such samples.
c. This sample of randomly chosen homes produced a 90% confidence interval for the
mean price in Orange County of ($233954, $246046). Does this interval provide evidence
that single-family home prices are unusually high in this county? Explain briefly.
d. Suppose we want to collect a new sample. How many homes must we survey to have
90% confidence of estimating the mean local price to within $2000?

Accepted Answer

The answer of Housing costs A government report on housing...

Question 14

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.

Accepted Answer

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

Question 15

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 16

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 17

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.

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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 20

The average American sees 3.9 movies at the theater each year. A curious student polls 30 friends and family over the course of a week. He finds that his friends have seen an average of 4.5 movies with a standard deviation of 1.2 movies.
-Find and interpret a 95% confidence interval for this sample.

Accepted Answer

The answer of The average American sees 3.9 movies at...

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

A P-value indicates

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?

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.

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.