8.1 EXERCISES 424 CHAPTER 8 Hypothesis Testing with Two Samples For Extra Help: MyLab® Statistics Building Basic Skills and Vocabulary 1. What is the difference between two samples that are dependent and two samples that are independent? Give an example of each. 2. Explain how to perform a two-sample z@test for the difference between two population means using independent samples with s1 and s2 known. 3. Describe another way you can perform a hypothesis test for the difference between the means of two populations using independent samples with s1 and s2 known that does not use rejection regions. 4. What conditions are necessary in order to use the z@test to test the difference between two population means? Independent and Dependent Samples In Exercises 5–8, classify the two samples as independent or dependent and justify your answer. 5. Sample 1: The maximum bench press weights for 53 football players Sample 2: The maximum bench press weights for the same 53 football players after completing a weight lifting program 6. Sample 1: The IQ scores of 60 females Sample 2: The IQ scores of 60 males 7. Sample 1: The average speed of 23 powerboats built using one hull design Sample 2: The average speed of 14 powerboats built using a different hull design 8. Sample 1: The commute times of 10 workers when they use their own vehicles Sample 2: The commute times of the same 10 workers when they use public transportation In Exercises 9 and 10, use the TI-84 Plus display to make a decision to reject or fail to reject the null hypothesis at the level of significance. Make your decision using the standardized test statistic and using the P-value. Assume the sample sizes are equal. 9. a = 0.05 10. a = 0.01 μ1≠μ2 z=2.956485408 p=0.0031118068 x1=2500 x2=2425 n1=120 2-SampZTest μ1>μ2 z=1.941656065 p=0.0260893059 x1=44 x2=42 n1=50 2-SampZTest In Exercises 11–14, test the claim about the difference between two population means m1 and m2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. 11. Claim: m1 = m2; a = 0.1 Population statistics: s1 = 3.4 and s2 = 1.5 Sample statistics: x1 = 16, n1 = 29 and x2 = 14, n2 = 28
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