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

Question 1

Answer 1

D

Question 2

Answer 2

B

Question 3

The power of a test is measured by its capability of

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

Answer 3

C

Question 4

Which of the following would be an appropriate null hypothesis?

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

Question 5

Which of the following would be an appropriate null hypothesis?

A) The population proportion is less than 0.65.
B) The sample proportion is less than 0.65.
C) The population proportion is not less than 0.65.
D) The sample proportion is no less than 0.65.

Question 6

Question 7

True or False: For a given level of significance, if the sample size is increased but the summary
statistics remain the same, the probability of committing a Type II error will increase.

Question 8

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

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

Question 9

Question 10

Question 11

A Type I error is committed when

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

Question 12

If a researcher rejects a true null hypothesis, she has made a _______error.

Question 13

If an economist wishes to determine whether there is evidence that mean family income in a
Community equals $50,000

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

Question 14

A Type II error is committed when

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

Question 15

True or False: For a given level of significance, if the sample size is increased but the summary
statistics remain the same, the probability of committing a Type I error will increase.

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

Question 17

Question 18

If an economist wishes to determine whether there is evidence that mean family income in a
Community exceeds $50,000

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

Question 19

True or False: For a given sample size, the probability of committing a Type II error will increase
when the probability of committing a Type I error is reduced.

Question 20

Which of the following would be an appropriate alternative hypothesis?

A) The population proportion is less than 0.65.
B) The sample proportion is less than 0.65.
C) The population proportion is not less than 0.65.
D) The sample proportion is not less than 0.65.

Question 21

If a researcher does not reject a false null hypothesis, she has made a _______error.

Question 22

Question 23

Question 24

Question 25

Question 26

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 level of significance is the maximum risk we are willing to accept in making a Type I error.
C)
D) The significance level is another name for Type II error.

Question 27

Question 28

Question 29

The power of a statistical test is

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

Question 30

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

If a researcher does not reject a true null hypothesis, she has made a _______decision.

Question 37

Question 38

If a researcher rejects a false null hypothesis, she has made a _______decision.

Question 39

Question 40

Question 41

The marketing manager for an automobile manufacturer is interested in determining the
Proportion of new compact-car owners who would have purchased a GPS navigation system 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 GPS navigation system.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 reach?

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

Question 42

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

Question 43

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
Greater than 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) 0.3577
B) 0.1423
C) 0.0780
D) 0.02

Question 44

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

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

Question 45

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
Referring to Scenario 9-1, what critical value should the manager use to determine the rejection
Region?

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

Question 46

A pizza 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 have a favorable view of its brain.It conducts a telephone poll of 300 randomly selected
Households in the area and finds that 96 have a favorable view.The pizza chain's conclusion from
The hypothesis test using a 5% level of significance is:

A) to open a new store.
B) not 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 47

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
Greater than 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:

Question 48

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

Question 49

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
Referring to Scenario 9-1, state the alternative hypothesis for this study.

Question 50

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

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

Question 51

A pizza 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 have a favorable view of its brain.It conducts a telephone poll of 300 randomly selected
Households in the area and finds that 96 have a favorable view.The value of the test statistic in
This problem is approximately equal to:

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

Question 52

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
Referring to Scenario 9-1, the parameter the manager is interested in is:

A) the mean number of defective light bulbs per case produced at the plant.
B) the mean number of defective light bulbs per case among the 46 cases.
C) the mean number of defective light bulbs per case produced during the morning shift.
D) the proportion of cases with defective light bulbs produced at the plant.

Question 53

A pizza 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 have a favorable view of its brain.It conducts a telephone poll of 300 randomly selected
Households in the area and finds that 96 have a favorable view.The decision on the hypothesis
Test using a 5% level of significance is:

Question 54

A pizza 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 have a favorable view of its brain.It conducts a telephone poll of 300 randomly selected
Households in the area and finds that 96 have a favorable view.The p-value associated with the
Test statistic in this problem is approximately equal to:

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

Question 55

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
Greater than 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 have a level of significance at 0.01
What conclusion can she make?

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

Question 56

The value that separates a rejection region from a non-rejection region is called the _______.

Question 57

A pizza 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 have a favorable view of its brain.It conducts a telephone poll of 300 randomly selected
Households in the area and finds that 96 have a favorable view.State the test of hypothesis that is
Of interest to the pizza chain.

Question 58

An entrepreneur is considering the purchase of a coin-operated laundry.The current owner claims
That over the past 5 years, the mean daily revenue was $675 with a population standard deviation
Of $75.A sample of 30 days reveals a daily mean revenue of $625.If you were to test the null
Hypothesis that the daily mean 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 mean revenue was $675.
B) There is not enough evidence to conclude that the daily mean revenue was not $675.
C) There is enough evidence to conclude that the daily mean revenue was $675.
D) There is enough evidence to conclude that the daily mean revenue was not $675.

Question 59

A manager of the credit department for an oil company would like to determine whether the mean
Monthly balance of credit card holders is equal to $75.An auditor selects a random sample of 100
Accounts and finds that the mean 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 mean 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 population mean
D) t-test of a population proportion

Question 60

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

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

Question 61

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
True or False: Referring to Scenario 9-1, the manager can conclude that there is sufficient
evidence to show that the mean number of defective bulbs per case is greater than 20 during the
morning shift with no more than a 1% probability of incorrectly rejecting the true null hypothesis.

Question 62

True or False: The smaller the p-value, the stronger is the evidence against the null hypothesis.

Question 63

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
True or False: Referring to Scenario 9-1, the evidence proves beyond a doubt that the mean
number of defective bulbs per case is greater than 20 during the morning shift.

Question 64

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
True or False: Referring to Scenario 9-1, the null hypothesis would be rejected.

Question 65

True or False: In testing a hypothesis, you should always raise the question concerning the
purpose of the study, survey or experiment.

Question 66

True or False: In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test.

Question 67

True or False: A sample is used to obtain a 95% confidence interval for the mean of a population.
The confidence interval goes from 15 to 19.If the same sample had been used to test the null
hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the
mean of the population differs from 20, the null hypothesis could be rejected at a level of
significance of 0.05.

Question 68

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
True or False: Referring to Scenario 9-1, the null hypothesis would be rejected if a 5% probability
of committing a Type I error is allowed.

Question 69

True or False: A sample is used to obtain a 95% confidence interval for the mean of a population.
The confidence interval goes from 15 to 19.If the same sample had been used to test the null
hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the
mean of the population differs from 20, the null hypothesis could be rejected at a level of
significance of 0.10.

Question 70

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
True or False: Referring to Scenario 9-1, if these data were used to perform a two-tail test, the p-
value would be 0.042.

Question 71

True or False: The statement of the null hypothesis always contains an equality.

Question 72

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
True or False: Referring to Scenario 9-1, the null hypothesis would be rejected if a 1% probability
of committing a Type I error is allowed.

Question 73

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
True or False: Referring to Scenario 9-1, the manager can conclude that there is sufficient
evidence to show that the mean number of defective bulbs per case is greater than 20 during the
morning shift with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

Question 74

True or False: The larger the p-value, the more likely you are to reject the null hypothesis.

Question 75

True or False: A sample is used to obtain a 95% confidence interval for the mean of a population.
The confidence interval goes from 15 to 19.If the same sample had been used to test the null
hypothesis that the mean of the population is equal to 18 versus the alternative hypothesis that the
mean of the population differs from 18, the null hypothesis could be rejected at a level of
significance of 0.05.

Question 76

True or False: A sample is used to obtain a 95% confidence interval for the mean of a population.
The confidence interval goes from 15 to 19.If the same sample had been used to test the null
hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the
mean of the population differs from 20, the null hypothesis could be rejected at a level of
significance of 0.02.

Question 77

SCENARIO 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random
sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to
know if the mean number of defective bulbs per case is greater than 20 during the morning shift.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 cases:
True or False: Referring to Scenario 9-1, the manager can conclude that there is sufficient
evidence to show that the mean number of defective bulbs per case is greater than 20 during the
morning shift using a level of significance of 0.10.

Question 78

True or False: A proper methodology in performing hypothesis tests is to ask whether a random
sample can be selected from the population of interest.

Question 79

True or False: The test statistic measures how close the computed sample statistic has come to the
hypothesized population parameter.

Question 80

True or False: A sample is used to obtain a 95% confidence interval for the mean of a population.
The confidence interval goes from 15 to 19.If the same sample had been used to test the null
hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the
mean of the population differs from 20, the null hypothesis could be accepted at a level of
significance of 0.01.