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

Question 1

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 1

rejecting a null hypothesis that is false.

Question 2

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

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

Answer 2

95%.

Question 3

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

Answer 3

Type I

Question 4

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

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

Question 5

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 no less than 0.65.
D) The sample proportion is no less than 0.65.

Question 6

If a researcher accepts a false null hypothesis, she has made a ________ error.

Question 7

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 no less than 0.65.
D) The sample proportion is no less than 0.65.

Question 8

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

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

Question 9

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

Question 10

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

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

Question 11

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 12

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 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

If a researcher accepts a true null hypothesis, she has made a ________ decision.

Question 15

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 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

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

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

Question 18

A Type II error is committed when

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

Question 19

A Type I error is committed when

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

Question 20

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

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

Question 21

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean 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: = 52, S = 22. Using the sample information provided, calculate the value of the test statistic.

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

Question 22

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) 0.3577
B) 0.1423
C) 0.0780
D) 0.02

Question 23

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 α = 0.10?

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

Question 24

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 α = 0.025?

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

Question 25

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

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

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) The significance level is also called the α level.
D) The significance level is another name for Type II error.

Question 27

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

Question 28

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean 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: = 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)
B)
C)
D)

Question 29

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

Question 30

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean 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: = 52, S = 22. Suppose the alternative we wanted to test was H₁ : μ < 60. State the correct rejection region for α = 0.05.

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

Question 31

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean 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: = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following conclusions is correct?

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

Question 32

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 α = 0.05?

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

Question 33

The symbol for the power of a statistical test is

A) α.
B) 1 - α.
C) β.
D) 1 - β.

Question 34

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 < -2.3263.
B) Reject H₀ if t < -2.5758.
C) Reject H₀ if t > 2.3263.
D) Reject H₀ if t > 2.5758.

Question 35

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean 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: = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following decisions is correct?

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

Question 36

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

Question 37

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 38

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 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 not over 30.

Question 39

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 40

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

Question 41

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 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 42

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

Question 43

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 9-1, the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

Question 44

A major DVD 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 DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. 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 45

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 9-1, the null hypothesis would be rejected.

Question 46

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 47

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 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 a population mean
D) t-test of a population proportion

Question 48

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a side curtain 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 side curtain 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 mean
B) Z-test of a population proportion
C) t-test of population mean
D) t-test of a population proportion

Question 49

A major DVD 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 DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The decision on the hypothesis test using a 3% level of significance is

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

Question 50

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a side curtain 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 side curtain 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 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 not 0.30.
D) There is not sufficient evidence that the proportion is not 0.30.

Question 51

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 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 52

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 9-1, the null hypothesis would be rejected if a 5% probability of committing a Type I error is allowed.

Question 53

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 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 a population mean
D) t-test of a population proportion

Question 54

A major DVD 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 DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. State the test of interest to the rental chain.

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

Question 55

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 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 56

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 9-1, state the alternative hypothesis for this study.

Question 57

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 mean balance is different from $75 and decided to reject the null hypothesis, what conclusion could you draw?

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 58

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

Question 59

A major DVD 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 DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. 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 60

A major DVD 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 DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The rental chain's conclusion from the hypothesis test using a 3% 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 61

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 9-1, the lowest level of significance at which the null hypothesis can be rejected is ________.

Question 62

"Is the intended sample size large enough to achieve the desired power of the test for the level of significance chosen?" should be among the questions asked when performing a hypothesis test.

Question 63

"What conclusions and interpretations can you reach from the results of the hypothesis test?" is not an important question to ask when performing a hypothesis test.

Question 64

Suppose, in testing a hypothesis about a proportion, the p-value is computed to be 0.034. The null hypothesis should be rejected if the chosen level of significance is 0.01.

Question 65

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

Question 66

The statement of the null hypothesis always contains an equality.

Question 67

Suppose, in testing a hypothesis about a proportion, the p-value is computed to be 0.043. The null hypothesis should be rejected if the chosen level of significance is 0.05.

Question 68

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 9-1, the evidence proves beyond a doubt that the mean number of defective bulbs per case is over 20 during the morning shift.

Question 69

In instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this has proven that the null hypothesis is true.

Question 70

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

Question 71

In instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this does not prove that the null hypothesis is true.

Question 72

In testing a hypothesis, you should always raise the question on the purpose of the study, survey or experiment.

Question 73

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 9-1, if these data were used to perform a two-tail test, the p-value would be 0.042.

Question 74

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

Question 75

Suppose, in testing a hypothesis about a proportion, the Z test statistic is computed to be 2.04. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tail test is used.

Question 76

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is over 20 during the morning shift using a level of significance of 0.10.

Question 77

In conducting research, you should document both good and bad results.

Question 78

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is over 20 during the morning shift with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

Question 79

You should report only the results of hypothesis tests that show statistical significance and omit those for which there is insufficient evidence in the findings.

Question 80

TABLE 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 over 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:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: H₀ : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
Referring to Table 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is over 20 during the morning shift with no more than a 1% probability of incorrectly rejecting the true null hypothesis.