Exam 11: Nonparametric Tests Online and CD Only

Perform a runs test for randomness. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A pitching machine throws baseballs that are either strikes (S)or balls (B). A coach records whether each ball thrown during batting practice is a strike or a ball. Can you conclude that the sequence of pitches is random? Use $\alpha$ = 0.05. B B S B S S B B S B B B B S B S S S S S B B B B S B B S B B B S S S B S S S B B B B B S S S S S S S B

A government agency claims that the median hourly wages for workers at fast food restaurants in the western U.S. is $6.55. In a random sample of 100 workers, 68 were paid less than $6.55, 10 were paid $6.55, and the rest more than $6.55. Find the test statistic z to test the governmentʹs claim.

The drama department at a college asked professors and students in the drama department to rank 8 actors according to their performance. The data are listed below. A 10 is the highest ranking and a 1 the lowest Ranking. Find the test statistic to test the claim of no correlation between the rankings. Actor 1 2 3 4 5 6 7 8 Professors 2 3 6 10 8 1 5 4 Students 4 3 1 4 5 7 9 6

The drama department at a college asked professors and students in the drama department to rank 8 actors according to their performance. The data are listed below. A 10 is the highest ranking and a 1 the lowest Ranking. Find the critical value to test the claim of no correlation between the rankings. Use $\alpha$ = 0.05. Actor 1 2 3 4 5 6 7 8 Professors 2 3 6 10 8 1 5 4 Students 4 3 1 4 5 7 9 6

A pitching machine throws baseballs that are either strikes (S)or balls (B). A coach records whether each ball thrown during batting practice is a strike or a ball. Find the standardized test statistic z to test for randomness. B B S B S S B B S B B B B S B S S S S S B B B B S B B S B B B S S S B S S S B B B B B S S S S S S S

The table below lists the verbal and math SAT scores of 10 students selected at random. Find the test statistic $\mathrm { r } _ { \mathrm { S } }$ to test the claim of no correlation between verbal and math SAT scores. Verbal 395 480 485 390 470 Math 480 550 575 510 560 Verbal 500 400 450 520 410 Math 525 610 530 400 410

Perform the indicated Wilcoxon test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -In a study of the effectiveness of physical exercise on weight loss, 20 people were randomly selected to participate in a program for 30 days. Use the Wilcoxon signed-rank test to test the claim that exercise has no effect on weight loss. Use $\alpha = 0.02$ Weight Before Program (in Pounds) 178 210 156 188 193 225 190 165 168 200 Weight After Program (in Pounds) 182 205 156 190 183 220 195 155 165 200 Weight Before Program (in Pounds) 186 172 166 184 225 145 208 214 148 174 Weight After Program (in Pounds) 180 173 165 186 240 138 203 203 142 170

A club professional at a major golf course claims that the course is so tough that even professional golfers rarely break par of 73. The scores from a random sample of 20 professional golfers are listed below. Find the Test statistic x to test the club professionalʹs claim. 72 70 73 73 76 75 67 79 73 78 70 72 74 74 81 79 73 75 76 66

Perform the indicated sign test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -One hundred people go on a special diet with the intention of losing weight. At the end of 6 weeks, 59 lost weight, 27 gained weight and the rest remained the same. Test the hypothesis that the diet is effective in reducing weight. Use $\alpha$ = 0.05. (Note: The diet will be effective if at least 50% lose weight.)

Perform the indicated Wilcoxon test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A random sample of nine students took the SAT test. and later on retook the test after taking a test preparation course. Their scores are listed below. Use the Wilcoxon signed-rank test to test the claim that the test preparation has no effect on their scores. Use $\alpha = 0.05 \text {. }$ Student 1 2 3 4 5 6 7 8 9 Before Score 820 1180 840 1080 850 1010 1160 940 980 After Score 840 1180 830 1120 880 1020 1150 980 1000

Perform the indicated Wilcoxon test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A local school district is concerned about the number of school days missed by its teachers due to illness. A random sample of 10 teachers is selected. The numbers of absences in one year are recorded. An incentive program is then offered in an attempt to reduce the absences. The numbers of absences in the year after the incentive program are recorded. The results are listed below. Use the Wilcoxon signed-rank test to test the claim that the incentive program is effective in reducing the number of days missed by teachers. Use $\alpha$ = 0.05. Teacher 1 2 3 4 5 6 7 8 9 10 Days Absent Before Incentive 8 4 7 3 10 5 2 8 3 7 Days Absent After Incentive 6 3 7 1 9 3 0 9 1 7

Perform the indicated sign test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A weight-lifting coach claims that weight-lifters can increase strength by taking vitamin E. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. Thirty days later, after regular training supplemented by vitamin E, they are tested again. The results are listed below. Use the sign test to test the claim that the vitamin E supplement is effective in increasing the athletesʹ strength. Use $\alpha = 0.05$ Athlete 1 2 3 4 5 6 7 8 9 Before 217 264 273 202 180 237 242 268 274 After 227 269 273 200 187 252 247 263 279

A government agency claims that the median hourly wages for workers at fast food restaurants in the western U.S. is $6.65. In a random sample of 100 workers, 68 were paid less than $6.65, 10 were paid $6.65, and the rest More than $6.65. Find the critical values to test the governmentʹs claim. Use $\alpha = 0.05$

The table below lists the verbal and math SAT scores of 35 students selected at random. Test the claim of no correlation between verbal and math SAT scores. Use $\alpha$ = 0.05. Verbal 295 380 385 290 370 400 300 350 420 310 Math 380 450 475 410 460 45 510 430 300 310 Verbal 295 340 410 520 360 400 660 530 700 610 Math 440 500 400 480 410 380 500 540 580 620 Verbal 290 470 510 380 390 550 420 430 330 370 Math 380 480 490 510 440 560 440 500 410 300 Verbal 430 390 530 380 390 Math 430 410 560 400 360

A researcher claims that the lifetimes (in hours)of fluorescent light bulbs are the same regardless of manufacturer. Random samples are selected from 3 different manufacturers. The data are listed below. Test the claim that the samples come from identical populations by using (a)a one-way ANOVA test and (b)a Kruskal-Wallis test. Compare the results. Use $\alpha$ = 0.05. Manufacturer 1 Manufacturer 2 Manufacturer 3 190220 180170 200210 235215 200175 195205 225230 175180 200205 215220 190185 205205

Perform the indicated Wilcoxon test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A pharmaceutical company wishes to test a new drug with the expectation of lowering cholesterol levels. Ten subjects are randomly selected and their cholesterol levels are recorded. The subjects were then placed on the drug for a period of 6 months, after which their cholesterol levels were tested again. The results (in mg per deciliter)are listed below. Use the Wilcoxon signed-rank test to test the companyʹs claim that the drug lowers cholesterol levels. Use $\alpha = 0.05 .$ Subject 1 2 3 4 5 6 7 8 9 10 Before 216 239 228 244 251 227 231 260 241 270 After 201 234 236 234 246 227 201 242 239 255

Use the sequence to find the values of $\mathrm { n } _ { 1 } \text { and } \mathrm { n } _ { 2 } \text {. }$ $\text { H H H L H L H L L H H L H L H L H L L H L H }$

Use the Spearman rank correlation coefficient to determine whether the correlation between the given variables is significant. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -The drama department at a college asked professors and students in the drama department to rank 8 actors according to their performance. The data are listed below. A 10 is the highest ranking and a 1 the lowest ranking. Test the claim that there is no correlation between professorsʹ and studentsʹ rankings. Use $\alpha = 0.05 \text {. }$ Actor 1 2 3 4 5 6 7 8 Professors 2 3 6 10 8 1 5 4 Students 4 3 1 4 5 7 9 6

A real estate agent surmises that the median rent for a one-bedroom apartment in a beach community in southern California is at least $1700 per month. The rents for a random sample of 15 one-bedroom apartments Are listed below. Find the test statistic x to test the agentʹs claim. \ 2000 \ 1950 \ 1400 \ 1575 \ 1435 \ 2450 \ 1875 \ 1370 \ 2090 \ 2700 \ 1695 \ 1700 \ 1775 \ 1700 \ 1480

Use the Spearman rank correlation coefficient to determine whether the correlation between the given variables is significant. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -The ages and systolic blood pressures of 9 randomly selected adults are given below. Can you conclude that there is a correlation between age and blood pressure? Use $\alpha$ = 0.05. Age 38 41 45 48 51 53 57 61 65 Blood Pressure () 116 120 123 131 142 145 148 150 152