Introduction to Probability and Statistics for Engineers and Scientists

540 Chapter 12:Nonparametric Hypothesis Tests

Sample Duplicates

6 1.96 1.98

7 1.95 2.03

8 1.96 2.03

9 1.92 2.01

10 2.00 2.12

Test the hypothesis, at the 5 percent level of significance, that the two measuring

instruments give equivalent results.

11.LetX 1 ,...,Xnbe a sample from the continuous distributionFhaving medianm;

and suppose we are interested in testing the hypothesisH 0 :m=m 0 against the

one-sided alternativeH 1 :m>m 0. Present the one-sided analog of the signed

rank test. Explain how thep-value would be computed.

12.In a study of bilingual coding, 12 bilingual (French and English) college students

are divided into two groups. Each group reads an article written in French, and

each answers a series of 25 multiple-choice questions covering the content of the

article. For one group the questions are written in French; the other takes the

examination in English. The score (total correct) for the two groups is:

Examination in French 11 12 16 22 25 25

Examination in English 10 13 17 19 21 24

Is this evidence at the 5 percent significance level that there is difficulty in

transferring information from one language to another?

13.Fifteen cities, of roughly equal size, are chosen for a traffic safety study. Eight of

them are randomly chosen, and in these cities a series of newspaper articles dealing

with traffic safety is run over a 1-month period. The number of traffic accidents

reported in the month following this campaign is as follows:

Treatment group 19 31 39 45 47 66 74 81

Control group 28 36 44 49 52 52 60

Determine the exactp-value when testing the hypothesis that the articles have

not had any effect.

14.Determine thep-value in Problem 13 by

(a) using the normal approximation;

(b) using a simulation study.