9. Hypothesis Testing for One Sample

In Exercises 9–12, refer to the sample data from the given exercises in Section 13-2. Use the Wilcoxon signed-ranks test for the claim about the median of a population.

 Exercise 15 “Cotinine in Smokers”

In Exercises 5–8, use the runs test with a significance level of α = 0.05. (All data are listed in order by row.)

Odd and Even Digits in Pi A New York Times article about the calculation of decimal places of π noted that “mathematicians are pretty sure that the digits of π are indistinguishable from any random sequence.” Given below are the first 25 decimal places of π. Test for randomness in the way that odd (O) and even (E) digits occur in the sequence. Based on the result, does the statement from the New York Times appear to be accurate?

In Exercises 9–12, use the runs test with a significance level of . (All data are listed in order by row.)

Testing for Randomness of Super Bowl Victories Listed below are the conference designations of teams that won the Super Bowl, where N denotes a team from the NFC and A denotes a team from the AFC. Do the results suggest that either conference is superior?

In Exercises 9–12, use the runs test with a significance level of . (All data are listed in order by row.)

Baseball World Series Victories Test the claim that the sequence of World Series wins by American League and National League teams is random. Given are recent results, with A = American League and N = National League.

Correcting the H Test Statistic for Ties In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H

First combine all of the sample data into one list, and then, in that combined list, identify the different groups of sample values that are tied. For each individual group of tied observations, identify the number of sample values that are tied and designate that number as t; then calculate T = t3 - t . Next, add the T values to get summation_T. The value of N is the total number of observations in all samples combined.

Listed below are performance (non-verbal) IQ scores from samples of subjects with low blood lead level, medium blood lead level, and high blood lead level (from Data Set 11 “IQ and Lead” in Appendix B). For the test of equal medians, find the value of the test statistic H using the methods of this section, and then find the corrected value of H using the above correction factor. Does the corrected value of H differ substantially from the uncorrected value?

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.

Exercise 7 in Section 9-1 “Buttered Toast Drop”

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.

Exercise 8 in Section 9-1 “Tennis Challenges”

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.

Exercise 9 in Section 9-1 “Cell Phones and Handedness”

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.