9. Hypothesis Testing for One Sample

Wilcoxon Tests What is the difference between the Wilcoxon signed-ranks test and the Wilcoxon rank-sum test?

Kruskal-Wallis Test What parametric test can also be conducted instead of the Kruskal-Wallis test? What is an advantage of using the Kruskal-Wallis test instead of the parametric test?

In Exercises 1–10, use the following weights (g) of Hershey’s Kisses from Data Set 38 “Candies” in Appendix B.

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tTest The bag of Hershey’s Kisses includes 75 of the candies. According to the label, the total weight is 340 g, so the candies should have a mean weight of 340/75 = 4.5333 g. Use the sample of weights listed above to test the claim that they are from a population with a mean of 4.5333 g. Use a 0.05 significance level with a t test. What does the conclusion suggest about the claim of 340 g printed on the label?

In Exercises 1–10, use the following weights (g) of Hershey’s Kisses from Data Set 38 “Candies” in Appendix B.

Sign Test Repeat Exercise 3 using the sign test to test the claim that the sample of weights is from a population with a median of 4.5333 g.

In Exercises 1–10, use the following weights (g) of Hershey’s Kisses from Data Set 38 “Candies” in Appendix B.

Wilcoxon Signed-Ranks Test Repeat Exercise 3 using the Wilcoxon signed-ranks test to test the claim that the sample of weights is from a population with a median of 4.5333 g.

In Exercises 1–10, use a 0.05 significance level with the indicated test. If no particular test is specified, use the appropriate nonparametric test from this chapter.

World Series The last 114 baseball World Series ended with 66 wins by American League teams and 48 wins by National League teams. Use the sign test to test the claim that in each World Series, the American League team has a 0.5 probability of winning.

Does a population have to be normally distributed to use the chi-square distribution?

What happens to the shape of the chi-square distribution as the degrees of freedom increase?

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.98, n = 26

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.99, n = 30

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.80, n = 51

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.99, n = 10

What are the two types of hypotheses used in a hypothesis test? How are they related?

Does failing to reject the null hypothesis mean that the null hypothesis is true? Explain.

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

In a hypothesis test, you assume the alternative hypothesis is true.