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**Homework 7 & 8 | Complete Solution**

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62. The following output from MINITAB presents the results of a hypothesis test.

1. What are the null and alternate hypotheses?

2. What is the value of the test statistic?

3. What is the P-value?

4. Do you reject H0 at the level?

22. A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. Following are the amounts measured in a simple random sample of eight cans.

• 11.96 12.10 12.04 12.13 11.98 12.05 11.91 12.03

1. If appropriate, perform a hypothesis test to determine whether the mean volume differs from 12 ounces. Use the level of significance. What do you conclude?

20. Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that more than 60% of those with diabetes who undergo this surgery will recover from diabetes? Use the level of significance.

28. The following MINITAB output presents the results of a hypothesis test for a population proportion p.

1. What are the null and alternate hypotheses?

2. What is the value of the sample proportion ?

3. Can H0 be rejected at the 0.05 level? Explain.

26. The New York City Department of Health and Mental Hygiene conducts regular inspections of restaurants. Each restaurant receives an inspection score, with lower scores indicating a more satisfactory inspection. Following are scores for the most recent inspection, as of October 2010, for random samples of 25 restaurants in the boroughs of Manhattan and Queens. Boxplots indicate that the samples come from populations that are approximately normal.

Manhattan

2 22 23 0 40 12 37 43 27

15 24 8 38 4 17 21 11 18

13 30 27 19 38 21 4

Queens

27 18 14 20 35 8 42 29 0

12 25 0 19 6 13 22 5 11

0 10 19 39 2 8 19

Source: New York City Dept. of Health and Mental Hygiene

Can you conclude that the mean scores differ between the two boroughs? Use the level of significance.

28. The concentration of benzene was measured in units of milligrams per liter for a simple random sample of five specimens of untreated wastewater produced at a gas field. The sample mean was 7.8 with a sample standard deviation of 1.4. Seven specimens of treated wastewater had an average benzene concentration of 3.2 with a standard deviation of 1.7. It is reasonable to assume that both samples come from populations that are approximately normal. Construct a 99% confidence interval for the reduction in benzene concentration after treatment.

36. The following computer output (from MINITAB) presents the results of a hypothesis test for the difference between two population means:

1. What is the alternate hypothesis?

2. Can H0 be rejected at the level? Explain.

3. How many degrees of freedom are there for the test statistic?

4. Use the simpler method to compute the degrees of freedom as the smaller of and .

22. An article in the Archives of Internal Medicine reported that in a sample of 244 men, 73 had elevated total cholesterol levels (more than 200 milligrams per deciliter). In a sample of 232 women, 44 had elevated cholesterol levels. Can you conclude that the proportion of people with elevated cholesterol levels differs between men and women? Use the level.

32. The following computer output (from MINITAB) presents the results of a hypothesis test on the difference between two proportions.

1. Is this a left-tailed test, a right-tailed test, or a two-tailed test?

2. What is the P-value?

3. Can H0 be rejected at the 0.05 level? Explain.

**Homework 7 & 8 | Complete Solution**

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