Deck 9: Fundamentals of Hypothesis Testing: One-Sample Tests

Question 1

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: $\overline{X}$ = 52, s = 22. Suppose the test statistic does fall in the rejection region at ? =

A) At ? = 0.05, there is sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues.
B) At ? = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.
C) At ? = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues.
D) At ? = 0.10, there is sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.

Answer 1

At ? = 0.10, there is sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.

Question 2

TABLE 9- 1
Microsoft Excel was used on a set of data involving the number of parasites found on 46 Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if the mean number of parasites per butterfly is over 20. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 Monarch butterflies:

$\begin{array}{llcc}\hline\bar{n}=46 ; \text {Arithmetic Mean} =28.00 ; \text {Standard Deviation} =25.92 ; \text { Standard Error}=3.82 ; \\\text {Null Hypothesis:} H_{0}: \mu \leq 20.000 ; \alpha=0.10 ; d f=45;\text { T Test Statistic }= 2.09;\\\text { One-Tailed Test Upper Critical Value} = 1.3006;\text { p-value} = 0.021; \text { Decision = Reject} \\\hline\end{array}$


-Referring to Table 9-1, what critical value should the biologist use to determine the rejection region?

A) 0.6800
B) 1.3006
C) 1.3011
D) 1.6794

Answer 2

1.3006

Question 3

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what decision should she make?

A) Accept H₀.
B) Fail to reject H₀.
C) Reject H₀.
D) We cannot tell what her decision should be from the information given.

Answer 3

Fail to reject H₀.

Question 4

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The decision on the hypothesis test using a 3% level of significance is

A) to fail to reject H₀ in favor of H₁.
B) to reject H₀ in favor of H₁.
C) to accept H₀ in favor of H₁.
D) We cannot tell what the decision should be from the information given.

Question 5

Which of the following would be an appropriate alternative hypothesis?

A) The sample proportion is less than 0.65.
B) The population proportion is no less than 0.65.
C) The sample proportion is no less than 0.65.
D) The population proportion is less than 0.65.

Question 6

TABLE 9-5
A bank tests the null hypothesis that the mean age of the bank's mortgage holders is less than or equal to 45, versus an alternative that the mean age is greater than 45. They take a sample and calculate a p-value of 0.0202.
Referring to Table 9-5, if the same sample was used to test the opposite one-tailed test, what would be that test's p-value?

A) 0.9596
B) 0.9798
C) 0.0202
D) 0.0404

Question 7

A Type II error is committed when

A) we don't reject a null hypothesis that is false.
B) we reject a null hypothesis that is false.
C) we don't reject a null hypothesis that is true.
D) we reject a null hypothesis that is true.

Question 8

Which of the following statements is not true about the level of significance in a hypothesis test?

A) The larger the level of significance, the more likely you are to reject the null hypothesis.
B) The significance level is another name for Type II error.
C) The significance level is also called the α level.
D) The level of significance is the maximum risk we are willing to accept in making a Type I error.

Question 9

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: $overline{X}$ = 52, s = 22. Suppose the test statistic does fall in the rejection region at ? =
0)05. Which of the following decision is correct?

A) At ? = 0.10, we do not reject H₀.
B) At ? = 0.05, we reject H₀.
C) At ? = 0.05, we do not reject H₀.
D) At ? = 0.05, we accept H₀.

Question 10

TABLE 9-6
The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. She performs a two-tailed test of the null hypothesis that the mean for the stressed oak furniture is 650. The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test.
Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650. What would be the p-value of this one-tailed test?

A) 0.840
B) 0.960
C) 0.040
D) 0.160

Question 11

TABLE 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes an average of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an average of 257.3 W.

-Referring to Table 9-3, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are

A) H₀ : µ ?257.3 versus H₁ : µ < 257.3.
B) H₀ : µ = 250 versus H₁ : µ ? 250.
C) H₀ : µ ? 250 versus H₁ : µ > 250.
D) H₀ : µ ? 250 versus H₁ : µ < 250.

Question 12

Which of the following would be an appropriate null hypothesis?

A) The mean of a population is greater than 55.
B) The mean of a population is equal to 55.
C) The mean of a sample is equal to 55.
D) Only A and C are true.

Question 13

We have created a 95% confidence interval for µ with the result (10, 15). What decision will we make if we test H₀ : µ = 16 versus H₁ : µ ? 16 at ? = 0.10?

A) Fail to reject H₀ in favor of H₁.
B) Accept H₀ in favor of H₁.
C) Reject H₀ in favor of H₁.
D) We cannot tell what our decision will be from the information given.

Question 14

TABLE 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.
Referring to Table 9-2, what is the "actual confidence coefficient"?

A) 0.84
B) 0.87
C) 0.16
D) 0.13

Question 15

We have created a 95% confidence interval for µ with the result (10, 15). What decision will we make if we test H₀ : µ = 16 versus H₁ : µ × 16 at ? = 0.025?

A) Reject H₀ in favor of H₁.
B) Fail to reject H₀ in favor of H₁.
C) Accept H₀ in favor of H₁.
D) We cannot tell what our decision will be from the information given.

Question 16

Which of the following would be an appropriate alternative hypothesis?

A) The mean of a population is equal to 55.
B) The mean of a population is greater than 55.
C) The mean of a sample is greater than 55.
D) The mean of a sample is equal to 55.

Question 17

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues
Used during a cold: $\overline{X}$ = 52, s = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.

A) H₀ : µ ? 60 and H₁: µ > 60
B) H0 : X ? 60 and H₁ : X < 60
C) H₀ : X = 52 and H₁: X ? 52
D) H₀ : µ ? 60 and H₁ : µ < 60

Question 18

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to

A) - 0.07.
B) - 2.33.
C) - 4.12.
D) - 1.86.

Question 19

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to be 99% confident in her decision, what rejection region should she use?

A) Reject H0 if t > 2.58.
B) Reject H0 if t < - 2.34.
C) Reject H₀ if t > 2.34.
D) Reject H₀ if t < - 2.55.

Question 20

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the p-value associated with the test statistic?

A) 0.02
B) 0.1423
C) 0.0780
D) 0.3577

Question 21

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are:

A) H₀ : $\overline{X}$ ? 30 versus H₁ : $\overline{X}$ > 30.
B) H₀ : µ ? 30 versus H₁ : µ < 30.
C) H₀ : $\overline{X}$ ? 30 versus H₁ : $\overline{X}$ < 30.
D) H₀ : µ ? 30 versus H₁ : µ > 30.

Question 22

If the Type I error (?) for a given test is to be decreased, then for a fixed sample size n

A) the Type II error (?) will increase.
B) the Type II error (?) will also decrease.
C) the power of the test will increase.
D) a one-tailed test must be utilized.

Question 23

The power of a statistical test is

A) the probability of rejecting H₀when it is true.
B) the probability of not rejecting H₀ when it is true.
C) the probability of rejecting H₀ when it is false.
D) the probability of not rejecting H₀ when it is false.

Question 24

The power of a test is measured by its capability of

A) rejecting a null hypothesis that is false.
B) rejecting a null hypothesis that is true.
C) not rejecting a null hypothesis that is true.
D) not rejecting a null hypothesis that is false.

Question 25

TABLE 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.
Referring to Table 9-2, what is the power of the test?

A) 0.87
B) 0.16
C) 0.13
D) 0.84

Question 26

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose that the test statistic is - 2.20. Can we conclude that H₀ should be rejected at the (a) α = 0.10, (b) α = 0.05, and (c) α = 0.01 level of Type I error?

A) (a) yes; (b) yes; (c) yes
B) (a) yes; (b) yes; (c) no
C) (a) no; (b) no; (c) yes
D) (a) no; (b) no; (c) no

Question 27

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The value of the test statistic in this problem is approximately equal to

A) 2.80.
B) 2.60.
C) 1.30.
D) 1.94.

Question 28

TABLE 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.
Referring to Table 9-2, what is the "actual level of significance" of the test?

A) 0.84
B) 0.87
C) 0.13
D) 0.16

Question 29

The symbol for the power of a statistical test is

A) 1 - ?.
B) 1 - ?.
C) ?.
D) ?.

Question 30

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use?

A) Z-test of a population proportion
B) t-test of a population proportion
C) Z-test of a population mean
D) t-test of population mean

Question 31

TABLE 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.
Referring to Table 9-2, what would be a Type II error?

A) saying that the person is a business major when in fact the person is an agriculture major
B) saying that the person is an agriculture major when in fact the person is a business major
C) saying that the person is an agriculture major when in fact the person is an agriculture major
D) saying that the person is a business major when in fact the person is a business major

Question 32

For a given level of significance (?), if the sample size n is increased, the probability of a Type II error (?)

A) will remain the same.
B) will increase.
C) will decrease.
D) cannot be determined.

Question 33

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if

A) a one-tailed test for µ is used.
B) a two-tailed test for µ is used.
C) Both of the previous statements are true.
D) None of the previous statements is true.

Question 34

TABLE 9-7
A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot." A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad at a 0.01 level of significance.
Referring to Table 9-7, the parameter the company officials is interested in is

A) the proportion of viewers who "like the ads a lot."
B) the mean number of viewers who "like the ads a lot."
C) the total number of viewers who "like the ads a lot."
D) the mean number of company officials who "like the ads a lot."

Question 35

A Type I error is committed when

A) we don't reject a null hypothesis that is false.
B) we don't reject a null hypothesis that is true.
C) we reject a null hypothesis that is false.
D) we reject a null hypothesis that is true.

Question 36

If, as a result of a hypothesis test, we reject the null hypothesis when it is false, then we have committed

A) no error.
B) a Type II error.
C) a Type I error.
D) an acceptance error.

Question 37

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The p-value associated with the test statistic in this problem is approximately equal to

A) 0.0026.
B) 0.0013.
C) 0.0100.
D) 0.0051.

Question 38

If we are performing a two-tailed test of whether µ = 100, the probability of detecting a shift of the mean to 105 will be ____the probability of detecting a shift of the mean to 110.

A) equal to
B) greater than
C) less than
D) not comparable to

Question 39

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues
Used during a cold: $\overline{X}$ = 52, s = 22. Suppose the alternative we wanted to test was H₁: µ < 60. State the correct rejection region for ? = 0.05.

A) Reject H₀ if t > 1.9842 or Z < - 1.9842.
B) Reject H₀ if t > 1.6604.
C) Reject H₀ if t < - 1.6604.
D) Reject H₀ if t < - 1.9842.

Question 40

You know that the level of significance (?) of a test is 5%, you can tell that the probability of committing a Type II error (?) is

A) 97.5%.
B) 95%.
C) unknown.
D) 2.5%.

Question 41

A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you were to conduct a test to determine whether the auditor should conclude that there is evidence that the average balance is different from $75, which test would you use?

A) Z-test of a population mean
B) Z-test of a population proportion
C) t-test of a population proportion
D) t-test of population mean

Question 42

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site. The conversion rate for a company's web site was 10.1% The web site at the company was redesigned in an attempt to increase its conversion rates. Samples of 200 browsers at the redesigned site were selected. Suppose that 24 browsers made a purchase. The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.

-Referring to Table 9-8, the null hypothesis will be rejected if the test statistics is

A) greater than 1.645.
B) greater than - 1.645.
C) less than 1.645.
D) less than - 1.645.

Question 43

TABLE 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.

-Referring to Table 9-2, what is the value of ??

A) 0.87
B) 0.84
C) 0.13
D) 0.16

Question 44

TABLE 9-6
The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. She performs a two-tailed test of the null hypothesis that the mean for the stressed oak furniture is 650. The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test.

-Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650. What would be the p-value of this one-tailed test?

A) 0.040
B) 0.840
C) 0.160
D) 0.960

Question 45

TABLE 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes an average of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an average of 257.3 W.
Referring to Table 9-3, the population of interest is

A) the mean power consumption in the 20 microwave ovens.
B) the power consumption in the 20 microwave ovens.
C) the mean power consumption in all such microwave ovens.
D) the power consumption in all such microwave ovens.

Question 46

If an economist wishes to determine whether there is evidence that average family income in a community equals $25,000

A) either a one-tailed or two-tailed test could be used with equivalent results.
B) a two-tailed test should be utilized.
C) a one-tailed test should be utilized.
D) none of the above

Question 47

An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals a daily average revenue of $625. If you were to test the null hypothesis that the daily average revenue was $675, which test would you use?

A) Z-test of a population proportion
B) Z-test of a population mean
C) t-test of a population proportion
D) t-test of population mean

Question 48

You know that the probability of committing a Type II error (þ) is 5%, you can tell that the power of the test is

A) 2.5%.
B) unknown.
C) 97.5%.
D) 95%.

Question 49

TABLE 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes an average of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an average of 257.3 W.
Referring to Table 9-3, what is the parameter of interest?
A) 250

A) the mean power consumption of the 20 microwave ovens
B) the mean power consumption of all such microwave ovens
D) 257.3

Question 50

If a test of hypothesis has a Type I error probability (α) of 0.01, we mean

A) if the null hypothesis is false, we reject it 1% of the time.
B) if the null hypothesis is false, we don't reject it 1% of the time.
C) if the null hypothesis is true, we don't reject it 1% of the time.
D) if the null hypothesis is true, we reject it 1% of the time.

Question 51

TABLE 9-7
A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot." A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad at a 0.01 level of significance.

-Referring to Table 9-7, the null hypothesis will be rejected if the test statistics is

A) greater than - 2.3263.
B) greater than 2.3263.
C) less than 2.3263.
D) less than- 2.3263.

Question 52

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30 and decided not to reject the null hypothesis, what conclusion could you draw?

A) There is not sufficient evidence that the proportion is not 0.30.
B) There is not sufficient evidence that the proportion is 0.30.
C) There is sufficient evidence that the proportion is 0.30.
D) There is sufficient evidence that the proportion is 0.30.

Question 53

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. State the test of interest to the rental chain.

A) H₀ : ? ? 0.32 versus H₁ : ? > 0.32
B) H₀ : ? ? 0.25 versus H₁ : ?> 0.25
C) H₀ : µ ? 5,000 versus H₁ : µ > 5,000
D) H₀ : ? ? 5,000 versus H₁ : ? > 5000

Question 54

Which of the following would be an appropriate null hypothesis?

A) The population proportion is no less than 0.65.
B) The sample proportion is less than 0.65.
C) The sample proportion is no less than 0.65.
D) The population proportion is less than 0.65.

Question 55

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site. The conversion rate for a company's web site was 10.1% The web site at the company was redesigned in an attempt to increase its conversion rates. Samples of 200 browsers at the redesigned site were selected. Suppose that 24 browsers made a purchase. The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.

-Referring to Table 9-8, the parameter the company officials is interested in is

A) the mean number of company officials who buy something in their visit to the company's web site.
B) the mean number of browsers who buy something in their visit to the company's web site.
C) the total number of browsers who buy something in their visit to the company's web site.
D) the proportion of browsers who buy something in their visit to the company's web site.

Question 56

A _____ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

A) test statistic
B) critical value
C) significance level
D) parameter

Question 57

A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you wanted to test whether the average balance is different from $75 and decided to reject the null hypothesis, what conclusion could you draw?

A) There is not evidence that the average balance is $75.
B) There is evidence that the average balance is $75.
C) There is evidence that the average balance is not $75.
D) There is not evidence that the average balance is not $75.

Question 58

Suppose we wish to test H₀ : µ ? 47 versus H₁ : µ > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?

A) We have made a correct decision
B) We have made a Type II error.
C) We have made a Type I error.
D) None of the above is correct.

Question 59

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what conclusion can she make?

A) There is not sufficient evidence that the mean age of her customers is over 30.
B) There is sufficient evidence that the mean age of her customers is not over 30.
C) There is not sufficient evidence that the mean age of her customers is not over 30.
D) There is sufficient evidence that the mean age of her customers is over 30.

Question 60

An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals a daily average revenue of $625. If you were to test the null hypothesis that the daily average revenue was $675 and decide not to reject the null hypothesis, what can you conclude?

A) There is not enough evidence to conclude that the daily average revenue was not $675.
B) There is enough evidence to conclude that the daily average revenue was $675.
C) There is enough evidence to conclude that the daily average revenue was not $675.
D) There is not enough evidence to conclude that the daily average revenue was $675.

Question 61

TABLE 9-4
A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with an average of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normal with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision.

-Referring to Table 9-4, the appropriate hypotheses are

A) H0 : µ > 7.4 versus H1 : µ ? 7.4.
B) H0 : µ ? 7.4 versus H1 : µ > 7.4.
C) H₀ : µ ? 7.4 versus H₁ : µ < 7.4.
D) H₀ : µ = 7.4 versus H₁ : µ ? 7.4.

Question 62

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose you reject the null hypothesis. What conclusion can you draw?

A) There is not sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90.
B) There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.
C) There is sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90.
D) There is not sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.

Question 63

TABLE 9- 1
Microsoft Excel was used on a set of data involving the number of parasites found on 46 Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if the mean number of parasites per butterfly is over 20. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 Monarch butterflies:
$\begin{array}{llcc} \hline n=46 ; \text { Arithmetic Mean }=28.00 ; \text { Standard Deviation }=25.92 ; \text { Standard Error }=3.82 ; \\\text { Null Hypothesis:} H_{0}: \mu \leq 20.000 ; \alpha=0.10 ; d f=45 ; T \text { Test Statistic} = 2.09;\\\text { One-Tailed Test Upper Critical Value} =1.3006 ;\text { p-value} =0.021 ; \text { Decision = Reject.}\\\hline\end{array}$


-Referring to Table 9-1, the power of the test is ______if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 18 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

Question 64

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: $\overline{X}$ = 52, s = 22. Using the sample information provided, calculate the value of the test statistic.

A) t = (52 - 60) / (22 / 10)
B) t = (52 - 60) / (22 / 100²)
C) t = (52 - 60) / (22 / 100)
D) t = (52 - 60) / 22

Question 65

We have created a 95% confidence interval for µ with the result (10, 15). What decision will we make if we test H₀ : µ = 16 versus H₁ : µ ? 16 at ? = 0.05?

A) Accept H₀ in favor of H₁.
B) Fail to reject H₀ in favor of H₁.
C) Reject H₀ in favor of H₁.
D) We cannot tell what our decision will be from the information given.

Question 66

If the p-value is less than α in a two-tailed test

A) a one-tailed test should be used.
B) no conclusion should be reached.
C) the null hypothesis should not be rejected.
D) the null hypothesis should be rejected.

Question 67

If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000

A) a one-tailed test should be utilized.
B) either a one-tailed or two-tailed test could be used with equivalent results.
C) a two-tailed test should be utilized.
D) none of the above

Question 68

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The rental chain's conclusion from the hypothesis test using a 3% level of significance is

A) not to open a new store.
B) to open a new store.
C) to delay opening a new store until additional evidence is collected.
D) We cannot tell what the decision should be from the information given.

Question 69

TABLE 9- 1
Microsoft Excel was used on a set of data involving the number of parasites found on 46 Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if the mean number of parasites per butterfly is over 20. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 Monarch butterflies:

$\begin{array}{llcc} \hline n=46 ; \text { Arithmetic Mean }=28.00 ; \text { Standard Deviation }=25.92 ; \text { Standard Error }=3.82 ; \\\text { Null Hypothesis:} H_{0}: \mu \leq 20.000 ; \alpha=0.10 ; d f=45 ; T \text { Test Statistic} = 2.09;\\\text { One-Tailed Test Upper Critical Value} =1.3006 ;\text { p-value} =0.021 ; \text { Decision = Reject.}\\\hline\end{array}$


-Referring to Table 9-1, the parameter the biologist is interested in is

A) the mean number of parasites on these 46 butterflies.
B) the mean number of butterflies in Pismo Beach State Park.
C) the proportion of butterflies with parasites.
D) the mean number of parasites on Monarch butterflies in Pismo Beach State Park.

Question 70

TABLE 9-7
A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot." A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad at a 0.01 level of significance.

-Referring to Table 9-7, what critical value should the company officials use to determine the rejection region?

Question 71

TABLE 9- 1
Microsoft Excel was used on a set of data $\begin{array}{llcc} \hline n=46 ; \text { Arithmetic Mean }=28.00 ; \text { Standard Deviation }=25.92 ; \text { Standard Error }=3.82 ; \\\text { Null Hypothesis:} H_{0}: \mu \leq 20.000 ; \alpha=0.10 ; d f=45 ; T \text { Test Statistic} = 2.09;\\\text { One-Tailed Test Upper Critical Value} =1.3006 ;\text { p-value} =0.021 ; \text { Decision = Reject.}\\\hline\end{array}$


-Referring to Table 9-1, the probability of committing a Type II error is _ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 24 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

Question 72

Suppose we want to test H₀ : µ ? 30 versus H₁ : µ < 30. Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H₀ in favor of H₁?

A) $\overline{X}$ = 27, s = 4
B) $\overline{X}$ = 32, s = 2
C) $\overline{X}$ = 26, s = 9
D) $\overline{X}$ = 28, s = 6

Question 73

TABLE 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.

-Referring to Table 9-2, what is the value of ??

A) 0.87
B) 0.16
C) 0.84
D) 0.13

Question 74

If a researcher rejects a false null hypothesis, she has made a(n) ______decision.

Question 75

TABLE 9-7
A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot." A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad at a 0.01 level of significance.

-Referring to Table 9-7, the lowest level of significance at which the null hypothesis can be rejected is ______.

Question 76

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site. The conversion rate for a company's web site was 10.1% The web site at the company was redesigned in an attempt to increase its conversion rates. Samples of 200 browsers at the redesigned site were selected. Suppose that 24 browsers made a purchase. The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
Referring to Table 9-8, what critical value should the company officials use to determine the rejection region?

Question 77

If a researcher rejects a true null hypothesis, she has made a(n)____ error.

Question 78

For a given sample size n, if the level of significance (α) is decreased, the power of the test

A) will decrease.
B) will increase.
C) will remain the same.
D) cannot be determined.

Question 79

TABLE 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.

-Referring to Table 9-2, what would be a Type I error?

A) saying that the person is an agriculture major when in fact the person is a business major
B) saying that the person is an agriculture major when in fact the person is an agriculture major
C) saying that the person is a business major when in fact the person is an agriculture major
D) saying that the person is a business major when in fact the person is a business major

Question 80

TABLE 9- 1
Microsoft Excel was used on a set of data involving the number of parasites found on 46 Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if the mean number of parasites per butterfly is over 20. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 Monarch butterflies:
$\begin{array}{llcc} \hline n=46 ; \text { Arithmetic Mean }=28.00 ; \text { Standard Deviation }=25.92 ; \text { Standard Error }=3.82 ; \\\text { Null Hypothesis:} H_{0}: \mu \leq 20.000 ; \alpha=0.10 ; d f=45 ; T \text { Test Statistic} = 2.09;\\\text { One-Tailed Test Upper Critical Value} =1.3006 ;\text { p-value} =0.021 ; \text { Decision = Reject.}\\\hline\end{array}$


-Referring to Table 9-1, the power of the test is____ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 30 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.