Bluman A.G. Elementary Statistics- A Step By Step Approach

686 Chapter 13 Nonparametric StatisticsApplying the Concepts 13–3School LunchA nutritionist decided to see if there was a difference in the number of calories served for lunchin elementary and secondary schools. She selected a random sample of eight elementary schoolsand another random sample of eight secondary schools in Pennsylvania. The data are shown.Elementary Secondary648 694589 730625 750595 810789 860727 702702 657564 7611. Are the samples independent or dependent?2. What are the hypotheses?3. What nonparametric test would you use to test the claim?4. What critical value would you use?5. What is the test value?6. What is your decision?7. What is the corresponding parametric test?8. What assumption would you need to meet to use the parametric test?9. If this assumption were not met, would the parametric test yield the same results?See page 717 for the answers.Exercises 13–31. What are the minimum sample sizes for the Wilcoxonrank sum test? n 1 and n 2 are each greater than or equal to 10.2. What are the parametric equivalent tests for theWilcoxon rank sum tests? The t test for independent samples3. What distribution is used for the Wilcoxon ranksum test? The standard normal distributionFor Exercises 4 through 11, use the Wilcoxon rank sumtest. Assume that the samples are independent. Alsoperform each of these steps.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.Use the traditional method of hypothesis testing unlessotherwise specified.4. Lengths of Prison Sentences A random sample ofmen and women in prison was asked to give the lengthof sentence each received for a certain type of crime. Ata 0.05, test the claim that there is no difference in thesentence received by each gender. The data (in months)are shown here.Males 8 12 6 14 22 27 32 24 26Females 7 5 2 3 21 26 30 9 4Males 19 15 13Females 17 23 12 11 165. Technology Proficiency Test The following are scoresfrom a technology proficiency test required of all newincoming students at a particular college. Use theWilcoxon rank sum test to see if there is a difference inscores between freshmen and transfer students at the0.05 level of significance.Freshmen 40 32 40 32 47 39 38 39 29 35 30Transfers 38 43 35 45 37 36 36 33 46 44 4113–16