1. Questions 1 and 2 Are Based on the Following Information

EF 507PS-Chapter 10FALL 2008

1. QUESTIONS 1 AND 2 ARE BASED ON THE FOLLOWING INFORMATION:

The supervisor of a production line believes that the average time to assemble an electronic component is 14 minutes. Assume that assembly time is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion was 11.6 minutes.

1.What are the appropriate null and alternative hypotheses?

A): 14 and : < 14

B): 14 and : > 14

C): = 14 and : 14

D): 14 and : = 14

2.Which of the following statements is most accurate?

A)Unable to reject the null hypothesis at 0.10.

B)Reject the null hypothesis at = 0.025, but not at = 0.05.

C)Reject the null hypothesis at = 0.05, but not at = 0.01.

D)Reject the null hypothesis at = 0.008.

QUESTIONS 3 THROUGH 6 ARE BASED ON THE FOLLOWING INFORMATION:

The manufacturer of a certain chewing gum claims that at least 80% of dentists surveyed prefer their type of gum. You decide to test their claim. You find that in a sample of 200 dentists, 74.1% do actually prefer their gum.

3.What are the null and alternative hypotheses for your test?

A): P 0.80 andP < 0.80

B): P = 0.80 and P 0.80

C): P 0.80 and P > 0.80

D): P > 0.80 and P 0.80

4.What would your decision rule be?

A)Reject if /.

B)Reject if /.

C)Reject if /.

D)Reject if / < - .

5. The value of the test statistic is

A)2.086.

B)1.444.

C)-2.086.

D)-1.444.

6. Which of the following statements is most accurate?

A)Unable to reject the null hypothesis at 0.10.

B)Reject the null hypothesis at = 0.05.

C)Reject the null hypothesis at = 0.10, but not 0.05.

D)Reject the null hypothesis at = 0.01.

7.A local transportation planning group is concerned about the lack of car-pooling on the part of commuters. They are afraid that the proportion of local drivers car-pooling is below the national average of 20%. A survey of 356 local drivers reveals that 18.7% of them car pool. What is your conclusion?

A)There is evidence that the proportion of local people car-pooling is not below the national average.

B)There is evidence that the proportion of local people car-pooling is below the national average.

C)There is no evidence that the proportion of local people car-pooling is below the national average.

D)There is no evidence that the proportion of local people car-pooling is not below the national average.

8.Suppose that you want to test: P = 0.53 vs.: P 0.53. The appropriate critical value would be:

A)

B)

C)

D)

9.Suppose that you want to test: P = 0.53 vs. : P 0.53. The test statistic would be:

A)( - ) /

B)(p - ) /

C) (-) /

D) (p - ) / [()(1 - ) /n ]

QUESTIONS 10 THROUGH 12 ARE BASED ON THE FOLLOWING INFORMATION:

The state lottery office claims that the average household income of those people playing the lottery is greater than $37,000. Assume that the distribution of household income of those people playing the lottery is normally distributed with a standard deviation of $5,756. Suppose that for a sample of 25 households, it is found that the average income was $36,243.

10. What are the appropriate null and alternative hypotheses?

A): = $37,000 and : > $37,000

B): = $37,000 and : $37,000

C): = $37,000 and : < $37,000

D): > $37,000 and : $37,000

11.What is the test statistic for this test?

A)t = 0.66.

B)Z = 0.66.

C)Z = 1.92.

D)t = 1.92.

12.What is the most accurate estimate of the p-value?

A)p-value > 0.10

B)p-value < 0.05

C)p-value < 0.10

D)p-value < 0.01

13.Suppose you have the following null and alternative hypotheses:: = 277 and :277, and you know that = 13.5. Take a random sample of 20 observations and let  = 0.05. For what values of sample mean will you reject the null hypothesis?

A)Sample mean > 282.9.

B)Sample mean < 271.1.

C)Sample mean > 282.9.

D)Sample mean > 271.1.

14.Which of the following statements is not true?

1. A test statistic is a function of the sample data on which the decision to reject or not reject the null hypothesis is to be based.
2. A rejection region consists of the set of all test statistic values for which the null hypothesis will be rejected.
3. A rejection region consists of the set of all test statistic values for which the alternative hypothesis will be rejected.
4. A good hypothesis-testing procedure is one for which the probability of making either type I or type II error is small.

15.The supervisor of a production line believes that the average time to assemble an electronic component is 14 minutes. Assume that assembly time is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion was 11.6 minutes. Is there evidence that the average amount of time required to assemble a component is something other than 14 minutes? Use = 0.01

16.The manufacturer of a certain chewing gum claims that four out of five dentists surveyed prefer their type of gum. You decide to test their claim. You find that in a sample of 200 doctors, 74.1% do actually prefer their gum. Is this evidence sufficient to doubt the manufacturer’s claim? Use = 0.025

17.The manufacturer of bags of cement claims that they fill each bag with at least 50.2 pounds of cement. Assume that the standard deviation for the amount in each bag is 1.2 pounds. The decision rule is adopted to shut down the filling machine if the sample mean weight for a sample of 40 bags is below 49.8. Suppose that the true mean weight of bags is 50 pounds. Using this decision rule, what is the probability of a Type II error?

18.An assembly line will be shut down for maintenance if the defect rate exceeds 2.3%. Suppose you adopt a 5% significance level and take a random sample 200 items off the assembly line and compute the proportions that are defective. For what values of the sample proportion will the assembly line be shut down?

QUESTIONS 19 THROUGH 22 ARE BASED ON THE FOLLOWING INFORMATION:

A pharmaceutical manufacturer is concerned that the mean impurity concentration in pills should not exceed 2%. It is known that from a particular production run impurity concentrations follow a normal distribution with standard deviation 0.32%. A random sample of 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 2.05%.

19.Test at the 5% level the null hypothesis that the population mean impurity concentration is 2% or less against the alternative that it is more than 2%.

20.Calculate the p-value for this test.

21.Suppose that the alternative hypothesis in Question 103 had been two-sided rather than one-sided. State, without doing the calculations, whether the p-value of the test would be higher than, lower than, or the same as that found in Question 104. Explain your reasoning.

22.In the context of this problem, explain why a one-sided alternative hypothesis is more appropriate than a two-sided alternative.

QUESTIONS 23 THROUGH 27 ARE BASED ON THE FOLLOWING INFORMATION:

Consider a problem with the hypothesis test vs., and the following decision rule: Reject if .

23. Rewrite the decision rule explicitly in terms of

24.Compute the probability of Type II error and the power of the test for = 4.06

25.Compute the probability of Type II error and the power of the test for = 4.04

26.Compute the probability of Type II error and the power of the test for = 4.01

27.Compute the probability of Type II error and the power of the test for = 4.0

QUESTIONS 28 THROUGH 30 ARE BASED ON THE FOLLOWING INFORMATION:

A wine producer claims that the proportion of its customers who cannot distinguish its product from frozen grape juice is at most 0.12. The producer decides to test this null hypothesis against the alternative that the true proportion is more than 0.12. The decision rule adopted is to reject the null hypothesis if the sample proportion who cannot distinguish between these two flavors exceeds 0.15.

28.If a random sample of 100 customers is chosen, what is the probability of a Type I error, using this decision rule?

29.If a random sample of 400 customers is selected, what is the probability of a Type I error, using this decision rule?

30.Suppose that the true proportion of customers who cannot distinguish between these flavors is 0.10. If a random sample of 100 customers is selected, what is the probability of a Type II error?

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