BackTest the claim about the mean of the differences for a population of paired data at the level of significance α. Assume the samples are random and dependent, and the populations are normally distributed.
Claim: μd<0 , α=0.05 , Sample statistics: d̄ =1.5 , sd=3.2 , n=14
In Exercises 1–4, classify the two samples as independent or dependent and justify your answer.
Sample 1: The retail prices of 20 motorcycles
Sample 2: The retail prices of 20 minivans
A personal trainer is studying whether a new stretching routine improves flexibility. She records the forward reach (in cm) of 6 clients before and after a 4-week program. Calculate the difference (after - before) for each client, the mean difference, and standard deviation.
Construct a 95% confidence interval for the mean difference of the population given the following information. Would you reject or fail to reject the claim that there is no difference in the mean?
In Exercises 17–24, use the indicated Data Sets from Appendix B. The complete data sets can be found at www.TriolaStats.com. Assume that the paired sample data are simple random samples and the differences have a distribution that is approximately normal.
Heights of Presidents Repeat Exercise 12 “Heights of Presidents” using all of the sample data from Data Set 22 “Presidents” in Appendix B.
Sign Test vs. Wilcoxon Signed-Ranks Test Using the data in Exercise 1, we can test for no difference between hospital admissions on Friday 6th and Friday 13th by using the sign test or the Wilcoxon signed-ranks test. In what sense does the Wilcoxon signed-ranks test incorporate and use more information than the sign test?
Using the Wilcoxon Signed-Ranks Test
In Exercises 5–8, refer to the sample data for the given exercises in Section 13-2. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have differences that come from a population with a median equal to zero. Use a 0.05 significance level.
Exercise 6 “Do Men and Women Talk the Same Amount?”
Rank Sums Exercise 12 uses Data Set 33 “Disney World Wait Times” in Appendix B, and the sample size for the 5:00 PM Tower of Terror wait times is n = 50.
a. If we have sample paired data with 50 nonzero differences, what are the smallest and largest possible values of T?
Rank Sums Exercise 12 uses Data Set 33 “Disney World Wait Times” in Appendix B, and the sample size for the 5:00 PM Tower of Terror wait times is n = 50.
b. If we have sample paired data with 50 nonzero differences, what is the expected value of T if the population consists of matched pairs with differences having a median of 0?
Rank Sums Exercise 12 uses Data Set 33 “Disney World Wait Times” in Appendix B, and the sample size for the 5:00 PM Tower of Terror wait times is n = 50.
c. If we have sample paired data with 50 nonzero differences and the sum of the positive ranks is 165, find the absolute value of the sum of the negative ranks.
Rank Sums Exercise 12 uses Data Set 33 “Disney World Wait Times” in Appendix B, and the sample size for the 5:00 PM Tower of Terror wait times is n = 50.
d. If we have sample paired data with n nonzero differences and one of the two rank sums is k, find an expression for the other rank sum.
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.
The Freshman 15 The “Freshman 15” refers to the belief that college students gain 15 lb (or 6.8 kg) during their freshman year. Listed below are weights (kg) of randomly selected male college freshmen (from Data Set 13 “Freshman 15” in Appendix B). The weights were measured in September and later in April. Use the sign test to test the claim that for the population of freshman male college students there is not a significant difference between the weights in September and the weights in the following April. What do you conclude about the Freshman 15 belief?
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.
Wilcoxon Signed-Ranks Test Repeat the preceding exercise using the Wilcoxon signed-ranks test.
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.
Rank Correlation Use the paired sample data from Exercise 1 and analyze the data using the rank correlation coefficient. What does the result tell us about the belief that college students gain 15 lb (or 6.8 kg) during their freshman year?
Independent and Dependent Samples In Exercises 5–8, classify the two samples as independent or dependent and justify your answer.
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