Question 1

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 0.300.
B)There is not sufficient evidence that the proportion is 0.300.
C)There is sufficient evidence that the proportion is 0.30.
D)There is not sufficient evidence that the proportion is not 0.30.

Accepted Answer

When you decide not to reject the null hypothesis in a hypothesis test, it means you have not found sufficient evidence to support the alternative hypothesis. Therefore, you conclude that there is not enough evidence to say the proportion is different from 0.30, but this does not prove the proportion is exactly 0.30.

Question 2

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 null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

Accepted Answer

Without the specific details of Scenario 9-1, it's impossible to definitively say whether the null hypothesis would be rejected at a 1% significance level. The decision to reject the null hypothesis depends on the p-value obtained from the statistical test in comparison to the chosen significance level (alpha). If the p-value is less than the alpha level (in this case, 1% or 0.01), then the null hypothesis would be rejected.

Question 3

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,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

Accepted Answer

We would use a Z-test of a population proportion since we are comparing a proportion (the proportion of new compact-car owners who would have purchased a GPS navigation system) to a known value (0.30). The sample size (200) is also large enough to satisfy the normality and independence assumptions required for the Z-test.

Question 4

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 null hypothesis would be rejected.

Accepted Answer

The p-value for the test is 0.036, which is less than the level of significance of 0.10. Therefore, the null hypothesis that the mean number of defective bulbs per case is 20 can be rejected in favor of the alternative hypothesis that the mean is greater than 20.

Question 5

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

Accepted Answer

This statement is true. The test statistic is calculated based on the difference between the sample statistic and the hypothesized population parameter, and reflects how likely it is that the sample was drawn from a population with that parameter value. A larger test statistic indicates a greater deviation from the hypothesized parameter, and may lead to rejection of the null hypothesis.

Question 6

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 is 0.01.

Accepted Answer

The null hypothesis should not be rejected at the 0.01 level of significance because the p-value (0.034) is greater than the significance level (0.01), indicating insufficient evidence to reject the null hypothesis at this level.

Question 7

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

Accepted Answer

The critical value for a two-tailed test with a significance level of 0.05 and 10 degrees of freedom is 1.3006.

Question 8

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 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.

Accepted Answer

Without the specific details of Scenario 9-1, such as statistical test results or confidence intervals, it's impossible to accurately conclude the sufficiency of evidence regarding the mean number of defective bulbs. The statement also incorrectly suggests a direct link between the probability of incorrectly rejecting the null hypothesis (Type I error rate) and the evidence sufficiency without providing the necessary statistical analysis outcomes.

Question 9

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 null hypothesis would be rejected if a 5% probability of committing a Type I error is allowed.

Accepted Answer

In Scenario 9-1, if a 5% probability of committing a Type I error is allowed, it means that the significance level (alpha) is set at 0.05. If the p-value obtained from the statistical test is less than or equal to 0.05, the null hypothesis would be rejected, indicating that the results are statistically significant at the 5% level.

Question 10

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 evidence proves beyond a doubt that the mean number of defective bulbs per case is greater than 20 during the morning shift.

Accepted Answer

The information provided in the scenario is not enough to make a conclusion about whether the mean number of defective bulbs per case is greater than 20 or not. The output only provides information about the sample mean, sample standard deviation, and sample size. The hypothesis test should be conducted to make a conclusion with a given level of significance.

Question 11

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 is 0.05.

Accepted Answer

Since the calculated p-value (0.043) is less than the chosen level of significance (0.05), the null hypothesis should be rejected. Therefore, the statement is true.

Question 12

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 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.

Accepted Answer

The p-value (0.019) is less than the level of significance (0.10) which means we reject the null hypothesis and conclude that the mean number of defective bulbs per case is greater than 20 during the morning shift. Additionally, the statement "no more than a 5% probability of incorrectly rejecting the true null hypothesis" refers to the level of significance (0.05), which is not applicable in this scenario as the manager chose a level of significance of 0.10.

Question 13

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.

Accepted Answer

The answer of SCENARIO 9-1
Microsoft Excel was used on a...

Question 14

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.

Accepted Answer

With a two-tail test at a significance level of 0.01, the critical Z values would be approximately ±2.58. Since 2.04 does not exceed 2.58, the null hypothesis should not be rejected based on this level of significance.

Question 15

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.

Accepted Answer

The answer of SCENARIO 9-1
Microsoft Excel was used on a...

Question 16

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 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.

Accepted Answer

The t-statistic value of 2.13 is greater than the critical value of 1.645 at a significance level of 0.10 with 45 degrees of freedom. Thus, the manager can reject the null hypothesis and 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.

Question 17

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

Accepted Answer

It is important to determine whether the alternative hypothesis is directional (one-tail) or non-directional (two-tail) as this will affect the calculation of the p-value and the interpretation of the results.

Question 18

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

Accepted Answer

In a two-tailed test, the p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. A p-value of 0.042 indicates that there is a 4.2% chance of observing such extreme results if the null hypothesis were true, which is a direct outcome of performing the test with the given data.

Question 19

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 .

Accepted Answer

The answer of SCENARIO 9-1
Microsoft Excel was used on a...

Question 20

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.

Accepted Answer

The sample proportion of households with a favorable view is 96/300 = 0.32. The sample size is 300, which is greater than 30. The population proportion is 0.5. The standard error of the proportion is sqrt(0.5*0.5/300) = 0.03. The z-score is (0.32 - 0.5)/0.03 = -6.67. The p-value is less than 0.05, so the null hypothesis is rejected. The pizza chain should open a new store.

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

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

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 is 0.01.

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 is 0.05.

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.

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