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

Question 1

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

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

Answer 1

95%.

Question 2

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.

Answer 2

D

Question 3

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.

Answer 3

A

Question 4

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

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

Question 5

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 6

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 7

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 8

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 9

If a test of hypothesis has a Type I error probability ( $\alpha$ ) of 0.01, it means that

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

Question 10

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 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 level of significance ( $\alpha$ ), if the sample size n is increased, the probability of a Type II error ( $\beta$ )

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

Question 13

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

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

Question 14

If the p-value is less than $\alpha$ 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 15

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

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

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

Question 17

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.

Question 18

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

Question 19

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 20

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 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 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 22

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: $\bar { X } = 52$ , S = 22.Suppose the alternative you wanted to test was H1 : $\mu$ $\lt$ 60 .State the correct rejection region for $\alpha$ = 0.05. a) Reject $H _ { 0 }$ if $t > 1.6604$ .
b) Reject $H _ { 0 }$ if $t < - 1.6604$ .
c) Reject $H _ { 0 }$ if $t > 1.9842$ or $Z < - 1.9842$ .
d) Reject $H _ { 0 }$ if $t < - 1.9842$ .

Question 23

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: $\bar { X } = 52$ , S = 22.Suppose the test statistic does fall in the rejection region at $\alpha$ = 0.05.Which of the following decision is correct? a) At $\alpha = 0.05$ , you do not reject $H _ { 0 }$ .
b) At $\alpha = 0.05$ , you reject $H _ { 0 }$ .
c) At $\alpha = 0.05$ , you do not reject $H _ { 0 }$ .
d) At $\alpha = 0.10$ , you do not reject $H _ { 0 }$ .

Question 24

Suppose we wish to test H0: $\mu$$\le$ 47 versus H1: $\mu$ > 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 25

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

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 $\alpha$ level.
D)The significance level is another name for Type II error.

Question 27

The symbol for the probability of committing a Type I error of a statistical test is

A) $\alpha$ .
B)1 - $\alpha$ .
C) $\beta$ .
D)1 - $\beta$ .

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: $\bar { X } = 52$ , S = 22.Suppose the test statistic does fall in the rejection region at $\alpha$ = 0.05.Which of the following conclusion is correct? a) At $\alpha = 0.05$ , there is not sufficient evidence to conclude that the mean number of tissues used during a cold is 60 tissues.
b) At $\alpha = 0.05$ , there is sufficient evidence to conclude that the mean number of tissues used during a cold is 60 tissues.
c) At $\alpha = 0.05$ , there is insufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.
d) At $\alpha = 0.10$ , there is sufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.

Question 29

The symbol for the level of significance of a statistical test is

A) $\alpha$ .
B)1 - $\alpha$ .
C) $\beta$ .
D)1 - $\beta$ .

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 numberof tissues used during a cold: , S = 22.Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.

Question 31

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

Question 32

The symbol for the probability of committing a Type II error of a statistical test is

A) $\alpha$ .
B)1 - $\alpha$ .
C) $\beta$ .
D)1 - $\beta$ .

Question 33

The symbol for the power of a statistical test is

A) $\alpha$ .
B)1 - $\alpha$ .
C) $\beta$ .
D)1 - $\beta$ .

Question 34

The symbol for the confidence coefficient of a statistical test is

A) $\alpha$ .
B)1 - $\alpha$ .
C) $\beta$ .
D)1 - $\beta$ .

Question 35

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 36

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 37

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 numberof tissues used during a cold: $\bar { X } = 52$ , S = 22.Using the sample information provided, calculate the value of the test statistic.

A)t =(52 - 60 ) / 2 2
B)t=(52 - 60 F) / (2 2 / 100 )
C)t =( 52 - 60 ) / (2 2 / 100 2 )
D)t = (52 - 60 ) / ( 2 2 / 1 0 )

Question 38

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

Question 39

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

Question 40

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 41

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 you conclude that H0 should be rejected at the (a) $\alpha$ = 0.10, (b) $\alpha$ = 0.05, and (c) $\alpha$ = 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 42

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 the20,000 households in the area have a favorable view of its brand.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:

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 43

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 reach?

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 44

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 the20,000 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 45

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 the20,000 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 46

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 47

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 the20,000 households in the area have a favorable view of its brand.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 48

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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-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 49

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 50

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 the20,000 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 51

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 52

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 53

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 shewants to have a level of significance at 0.01, what decision should she make?

A)Reject H0.
B)Reject H1.
C)Do not reject H0.
D)We cannot tell what her decision should be from the information given.

Question 54

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.Themanager 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 todetermine 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 55

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 56

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 shewants 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 57

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 58

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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-Referring to Scenario 9-1, state the alternative hypothesis for this study.

Question 59

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 60

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.If she wants to have a level of significance at 0.01, what rejection region should she use? .

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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-Referring to Scenario 9-1, the null hypothesis would be rejected if a 1%probability of committing a Type I error is allowed.

Question 62

The larger the p-value, the more likely you are to reject 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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-Referring to Scenario 9-1, the null hypothesis would be rejected.

Question 64

The smaller the p-value, the stronger is the evidence against the null hypothesis.

Question 65

The statement of the null hypothesis always contains an equality.

Question 66

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 thealternative 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 67

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

Question 68

Suppose, in testing a hypothesis about a mean, the p-value is computed to be 0.034.The null hypothesis should be rejected if the chosen level of significance is0.01.

Question 69

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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-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 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:
Referring to Scenario 9-1, the lowest level of significance at which the null hypothesis can be rejected is .

Question 71

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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-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 72

Suppose, in testing a hypothesis about a mean, 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 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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-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

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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-Referring to Scenario 9-1, the null hypothesis would be rejected if a 5%probability of committing a Type I error is allowed.

Question 75

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

Question 76

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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-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 77

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 thealternative 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 78

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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-Referring to Scenario 9-1, if these data were used to perform a two-tail test, the p-value would be 0.042.

Question 79

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: $n = 46 ;$ Arithmetic Mean $= 28.00 ;$ Standard Deviation $= 25.92 ;$ Standard Error $= 3.82 ;$
Null Hypothesis: $H _ { 0 } : \mu \leq 20 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ;
One-Tail Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject.

-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 80

Suppose, in testing a hypothesis about a mean, the p-value is computed to be 0.043.The null hypothesis should be rejected if the chosen level of significance is0.05.