Exam 13: Nonparametric Statistics

In a study of the effectiveness of physical exercise in weight reduction, 12 subjects followed a program of physical exercise for two months. Their weights (in pounds)before and after this program are shown in the table. Use a significance level of 0.05 to test the claim that the exercise program has no effect on weight. Before 162 190 188 152 148 127 195 164 175 156 180 136 After 157 194 179 149 135 130 183 168 168 148 170 138

A sample of 15 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. D D A A A A A A A A A A D D D

Construct a data set with n = 14 such that the sign test would fail to reject the null hypothesis that the median is equal to 50 while the t-test conclusion is to reject the null hypothesis of µ = 50.

Ten luxury cars were ranked according to their comfort levels and their prices. Make Comfort Price 5 1 B 8 7 C 9 3 D 1. 5 4 4 3 2 G 2 16 H 1 9 I 7 6 6 8 Find the rank correlation coefficient and test the claim of no correlation between comfort and price. Use a significance level of 0.05.

Provide an appropriate response. -Describe parametric and nonparametric tests. Explain why nonparametric tests are important.

Given that the rank correlation coefficient, rs, for 37 pairs of data is 0.373, test the claim of no correlation between the two variables. Use a significance level of 0.01.

The systolic blood pressure readings of ten subjects before and after following a particular diet for a month are shown in the table. Use a significance level of 0.01 to test the claim that the diet has no effect on systolic blood pressure. Subject A B C D E F G H I J Before 175 192 167 180 161 203 185 176 204 146 After 160 190 170 180 153 197 191 174 192 150

Fourteen people rated two brands of soda on a scale of 1 to 5. Brand A 2 3 2 4 3 1 2 Brand B 1 4 5 5 1 2 3 Brand A 5 4 2 1 1 4 3 Brand B 4 5 5 2 4 5 4 At the 5 percent level, test the null hypothesis that the two brands of soda are equally popular.

Test the sequence of digits below for randomness of odd and even digits. 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

Use the sample data below to find the rank correlation coefficient and test the claim of no correlation between math and verbal scores. Use a significance level of 0.05. Mathematics 347 440 327 456 427 349 377 398 425 Verbal 285 378 243 371 340 271 294 322 385

Provide an appropriate response. -List the advantages and disadvantages of nonparametric tests.

In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H by $1 - \frac { \sum \mathrm { T } } { \mathrm { N } ^ { 3 } - \mathrm { N } }$ For each group of tied observations, calculate $\mathrm { T } = \mathrm { t } ^ { 3 } - \mathrm { t }$ , where $\mathrm { t }$ is the number of observations that are tied withi the individual group. Find $\mathrm { t }$ for each group of tied values, then compute the value of $\mathrm { T }$ for each group, then add the T values to get $\sum \mathrm { T }$ . The total number of observations in all samples combined is N. Find the corrected value of $\mathrm { H }$ for the data below which represents test scores for three different groups. Group 1: 20 18 18 18 20 20 Group 2: 18 12 18 18 20 Group 3: 16 18 13 18 18

A researcher wishes to study whether a particular diet is effective in helping people to lose weight. 86 randomly selected adults were weighed before starting the diet and again after following the diet for one month. 47 people lost weight, 37 gained weight, and 2 observed no change in their weight. At the 0.01 significance level, test the claim that the diet is effective.

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. Use the sign test to test the claim that programmers do better on the mathematics portion of the test. Use a 0.05 level of significance. Mathematics 347 440 327 456 427 349 377 398 425 Verbal 285 378 243 371 340 271 294 322 385

Provide an appropriate response. -Define rank. Explain how to find the rank for data which repeats (for example, the data set: 4, 5, 5, 5, 7, 8, 12, 12, 15, 18).

The table below shows the weights (in pounds)of 6 randomly selected women in each of three different age groups. Use a 0.01 significance level to test the claim that the 3 age-group populations of weights are identical. 18-34 35-55 56 and older 119 123 140 134 147 128 114 135 59 125 110 134 153 154 120 138 163 116

Given that the rank correlation coefficient, rs, for 20 pairs of data is 0.809, test the claim of no correlation between the two variables. Use a significance level of 0.05.

The table below shows the lifetimes (in hours)of random samples of light bulbs of three different brands. Use a 0.01 significance level to test the claim that the samples come from identical populations. Brand A Brand B Brand C 190 182 203 220 170 210 230 203 199 215 175 200 224 178 196 231 181 197

Use a 0.05 level of significance to test the claim that the sequence of computer-generated numbers is random. Test for randomness above and below the mean. $8\quad7\quad5\quad7\quad3\quad9\quad1\quad8\quad0\quad4\quad3\quad8\quad4\quad6\quad2\quad3\quad9\quad7\quad5$

The heights of 16 randomly selected women are given below. Use a significance level of 0.05 to test the claim that the population median is equal to 64.0 inches. 62.9 61.9 66.4 68.5 63.7 64.0 65.2 67.0 70.2 65.3 64.0 60.3 64.3 66.9 65.0 63.8