Slide 13- 1Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Active Learning Lecture Slides For use with Classroom Response Systems

Elementary Statistics Eleventh Edition

and the Triola Statistics Series

by Mario F. Triola

Chapter 13: Nonparametric Statistics

Slide 13- 2Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Use the sign test to test the indicated claim.

A standard aptitude test is given to several randomly selected programmers and the scores are given below for the mathematics and verbal portions of the test. Test the claim that programmers do better on the mathematics portion of the test. Use a 0.05 level of significance.

Mathematics 347 440 327 456 427 349 377 398 425Verbal 285 378 243 371 340 271 294 322 385

A. Fail to reject the null hypothesis that math scores are equal to verbal scores.

B. Reject the null hypothesis that math scores are equal to verbal scores.

Slide 13- 3Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Use the sign test to test the indicated claim.

A standard aptitude test is given to several randomly selected programmers and the scores are given below for the mathematics and verbal portions of the test. Test the claim that programmers do better on the mathematics portion of the test. Use a 0.05 level of significance.

Mathematics 347 440 327 456 427 349 377 398 425Verbal 285 378 243 371 340 271 294 322 385

A. Fail to reject the null hypothesis that math scores are equal to verbal scores.

B. Reject the null hypothesis that math scores are equal to verbal scores.

Slide 13- 4Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Use the Wilcoxon signed-ranks test to test the given claim.

11 runners are timed at the 100-meter dash and are timed again one month after following a new training program. The times (in seconds) are shown in the table. Use a significance level of 0.05 to test the claim that the training has no effect on the times.

Before 12.1 12.4 11.7 11.5 11 11.8 12.3 10.8 12.6 12.7 10.7

After 11.9 12.4 11.8 11.4 11.2 11.5 12.0 10.9 12.0 12.2 11.1

A. Fail to reject the null hypothesis that the population of matched pairs has differences with a median equal to zero.

B. Reject the null hypothesis the population of matched pairs has differences with a median equal to zero.

Slide 13- 5Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Use the Wilcoxon signed-ranks test to test the given claim.

11 runners are timed at the 100-meter dash and are timed again one month after following a new training program. The times (in seconds) are shown in the table. Use a significance level of 0.05 to test the claim that the training has no effect on the times.

Before 12.1 12.4 11.7 11.5 11 11.8 12.3 10.8 12.6 12.7 10.7

After 11.9 12.4 11.8 11.4 11.2 11.5 12.0 10.9 12.0 12.2 11.1

A. Fail to reject the null hypothesis that the population of matched pairs has differences with a median equal to zero.

B. Reject the null hypothesis the population of matched pairs has differences with a median equal to zero.

Slide 13- 6Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Given the rank correlation coefficient, rs, for 39 pairs of data is 0.296, test the claim of no correlation between the variables. Use a significance level of 0.01.

A. There appears to be a correlation between the two variables.

B. There does not appear to be a correlation between the two variables.

Slide 13- 7Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Given the rank correlation coefficient, rs, for 39 pairs of data is 0.296, test the claim of no correlation between the variables. Use a significance level of 0.01.

A. There appears to be a correlation between the two variables.

B. There does not appear to be a correlation between the two variables.

Slide 13- 8Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

A true-false test has the following answer sequence:

T T T T F T F T F T F T T F T

T T F F F F F F F T F T F T F

Using a significance level of 0.05, use the runs test to test the null hypothesis that the sequence was random.

A. Fail to reject the null hypothesis of randomness.

B. Reject the null hypothesis of randomness.

Slide 13- 9Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

A true-false test has the following answer sequence:

T T T T F T F T F T F T T F T

T T F F F F F F F T F T F T F

Using a significance level of 0.05, use the runs test to test the null hypothesis that the sequence was random.

A. Fail to reject the null hypothesis of randomness.

B. Reject the null hypothesis of randomness.