Exam 13: Nonparametric Statistics

A researcher wishes to study whether music has any effect on the ability to memorize information. 87 randomly selected adults are given a memory test in a quiet room. They are then given a second memory test while listening to classical music. 62 people received a higher score on the second test, 24 a lower score, and 1 received the same score. At the 0.05 significance level, test the claim that the music has no effect on memorization skills.

A sample of 30 clock radios is selected in sequence from an assembly line. Each radio is examined and judged to be acceptable (A)or defective (D). The results are shown below. Test for randomness.

Provide an appropriate response. -Describe the sign test. What types of hypotheses is it used to test? What is the underlying concept?

When performing a rank correlation test, one alternative to using Table A-9 to find critical values is to compute them using this approximation: $r _ { S } = \pm \sqrt { \frac { t ^ { 2 } } { t ^ { 2 } + n - 2 } }$ where $t$ is the $t - s c o r e$ from Table $\mathrm { A } - 3$ corresponding to $n - 2$ degrees of freedom. Use this approximation to find critical values of $r _ { \mathrm { S } }$ for the case where $\mathrm { n } = 11$ and $\alpha = 0.01$ .

When performing a rank correlation test, one alternative to using Table A-9 to find critical values is to compute them using this approximation: $r _ { S } = \pm \sqrt { \frac { t ^ { 2 } } { t ^ { 2 } + n - 2 } }$ where $t$ is the $t$ -score from Table A-3 corresponding to $\mathrm { n } - 2$ degrees of freedom. Use this approximation to find critical values of $\mathrm { r } _ { \mathrm { S } }$ for the case where $\mathrm { n } = 17$ and $\alpha = 0.05$ .

A pollster interviews voters and claims that her selection process is random. Listed below is the sequence of voters identified according to gender. At the 0.05 level of significance, test her claim that the sequence is random according to the criterion of gender. ,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,

Provide an appropriate response. -Describe the Wilcoxon rank-sum test. What type of hypotheses is it used to test? What assumptions are made for this test? What is the underlying concept?

Provide an appropriate response. -Describe the rank correlation test. What types of hypotheses is it used to test? How does the rank correlation coefficient rs differ from the correlation coefficient r?

Provide an appropriate response. -Describe the Kruskal-Wallis test. What types of hypotheses is it used to test? What assumptions are made for this test?

Test the sequence of digits below for randomness above and below the value of 4.5. 0 4 7 3 6 0 9 7 4 8 7 2 8 5 7 3 9 6 4 6 4 7 9 1 6 1 9 5 8 3 7 8 5 7 3 5 2 9 3 8

Given that the rank correlation coefficient, rs, for 75 pairs of data is -0.783, test the claim of no correlation between the two variables. Use a significance level of 0.05.

A placement test is required for students desiring to take a finite mathematics course at a university. The instructor of the course studies the relationship between students' placement test score and final course score. A random sample of eight students yields the following data. Placement Score Final Course Score 38 63 90 41 95 54 51 32 86 93 74 60 60 61 57 89 Compute the rank correlation coefficient, rs, of the data and test the claim of no correlation between placement score and final course score. Use a significance level of 0.05.

Given that the rank correlation coefficient, rs, for 15 pairs of data is -0.623, test the claim of no correlation between the two variables. Use a significance level of 0.01.

Listed below are grade averages for randomly selected students with three different categories of high-school background. At the 0.05 level of significance, test the claim that the three groups come from identical populations. $\text { HIGH SCHOOL RECORD }$ Good Fair Poor 3.21 2.87 2.01 3.65 3.05 2.31 1.00 2.00 2.98 3.12 0.00 0.50 2.75 1.98 2.36

A researcher wishes to test whether a particular diet has an effect on blood pressure. The blood pressure of 25 randomly selected adults is measured. After one month on the diet, each person's blood pressure is again measured. For 16 people, the second blood pressure reading was lower than the first, and for 9 people, the second blood pressure reading was higher than the first. At the 0.01 significance level, test the claim that the diet has an effect on blood pressure.

The outcomes (odd number or even number)of a roulette wheel are shown below. Test for randomness of odd (O)and even (E)numbers. O E O E O E O E E O E E E E O E O O E O E E O E

A true-false test had 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 Test the null hypothesis that the sequence was random.

Answers to a questionnaire were in the following sequence. Test for randomness. N N N N Y Y Y N N N

When performing a rank correlation test, one alternative to using Table A-9 to find critical values is to compute them using this approximation: $r _ { S } = \pm \sqrt { \frac { t ^ { 2 } } { t ^ { 2 } + n - 2 } }$ where $t$ is the t-score from Table A-3 corresponding to $\mathrm { n } - 2$ degrees of freedom. Use this approximation to find critical values of $\mathrm { r } _ { \mathrm { S } }$ for the case where $\mathrm { n } = 7$ and $\alpha = 0.05$ .

An instructor gives a test before and after a lesson and results from randomly selected students are given below. At the 0.05 level of significance, test the claim that the lesson has no effect on the grade. Use Wilcoxon's signed-ranks test. Before 54 61 56 41 38 57 42 71 88 42 36 23 22 46 51 After 82 87 84 76 79 87 42 97 99 74 85 96 67 84 79