Review Exercises (week 12: Hypothesis Testing with Two Samples)

Review Exercises ( week 12: Hypothesis Testing with Two Samples)

In Exercises 1 4, use the given sample statistics (independent samples) to test the claim about the difference between two population means, and , at the given level of significance α.

1. Claim: . Sample statistics: and .

1. Claim: Sample statistics: and

1. Claim: Sample statistics: and

1. Claim: , Sample statistics: and

In Exercise 5, (a) identify the claim and state and , (b) identify the rejection region(s), (c) find the standardized test statistic, (d) decide whether to reject or fail to reject, the null hypothesis, and (e) interpret this decision in the context of the original claim.

1. In a fast food study, a nutritionist finds that the mean calorie content of 36 Arby’s fish sandwiches is 529 calories with a standard deviation of 43 calories. The mean calorie content of 41 McDonald’s fish sandwiches is 560 calories with standard deviation of 57 calories. At α=0.05, is there enough evidence for the nutritionist to conclude that the Arby’s sandwich has fewer calories than the McDonald’s sandwich?

In Exercises 6 and 7, use the given sample statistics to test the claim about the difference between two population means, and , at a given level of significance α. Assume the populations are approximately normally distributed.

1. Claim: Sample statistics: and Assume equal variances.

1. Claim: Sample statistics: and Assume variances are not equal.

In Exercise 8, (a) identify the claim and state and , (b) identify the rejection regions, (c) find the standardized test statistic, (d) decide whether to reject, or fail to reject, the null hypothesis, and (e) interpret this decision in the context of the original claim.

1. A real estate agent claims that there is no difference between the mean household incomes of two neighborhoods. The mean income of 12 households from the first neighborhood was $18,250 with a standard deviation of $1200. In the second neighborhood, 10 households had a mean income of $17,500 with a standard deviation of $950. Assume normal distributions and equal population variances. Test the claim at α=0.05.

In Exercises 9 and 10, classify the samples as independent or dependent. Explain your reasoning.

1. Sample 1: Maze completion times for 14 standard laboratory mice

Sample 2: Maze completion times for 14 laboratory mice bred for highest metabolic rate

1. Sample 1: Maze completion times for 43 mice

Sample 2: Maze completion times for those 43 mice after two weeks of maze practice

In Exercises 11 and 12, using a test for paired data, test the claim about the mean of the difference of the two populations at the given level of significance using the given statistics. Is the test right-tailed, left-tailed, or two-tailed? Assume the sample statistics are from populations that are normally distributed.

1. Claim: Statistics:

1. Claim: Statistics:

In Exercise 13, (a) identify the claim and state and , (b) find the critical values and identify the rejection regions, (c) calculate and , (d) use the t-test to find the standardized test statistic, (e) decide whether to reject, or fail to reject, the null hypothesis, and (f) interpret the decision in the context of the original claim. For each sample, assume the distribution of the population is normal.

1. A medical researcher wants to test the effects of calcium supplements on men’s blood pressure. As part of the study, 10 men are given a calcium supplement for 12 weeks. The researcher measures the men’s systolic blood pressure at the beginning and at the end of the 12-week study and records the results shown below. At α = 0.10, can the researcher claim that the men’s systolic blood pressure decreased?

Patient
Before
After	100	114	105	112	115	116	106	102	125	104

In Exercise 14, test the claim about the difference between two population proportions and at the given level of significance α and the given sample statistics. Is the test left-tailed, right-tailed, or two-tailed? Assume the sample statistics are from independent samples.

1. Claim: Sample statistics: and

In Exercise 15, (a) identify the claim and state and , 9b) use Table 4 to find the critical values and identify the rejection regions, (c) find the standardized test statistic, (d) decide whether to reject, or fail to reject, the null hypothesis, and (e)interpret the decision in the context of the original claim. Assume the samples are independent.

1. In 1991, in a random sample of 200 Canadians, 22 had college degrees. Out of 300 Canadians who were sampled in 1996, 40 had college degrees. At α = 0.10, can you reject the claim that the proportion of Canadians with college degrees was the same for both years?

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