Exam 11: Nonparametric Tests Online and CD Only

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 final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam are given below. Can you conclude that there is a correlation between scores on the test and time spent studying? Use $\alpha = 0.01 .$ Hours 7 9 6 12 6 8 8 9 10 7 Score 69 84 64 92 70 82 89 94 94 75

Verbal SAT scores for students randomly selected from two different schools are listed below. Use the Wilcoxon rank sum test to find R to test the claim that there is no difference in the scores from each school. School 1 School 2 580 550 800 520 470 710 510 780 560 460 740 620 610 810 640 720 580 560 620 760 780 660 670 570

Nine students took the SAT test. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Use the Wilcoxon signed-rank test to find the test statistic Ws to test the claim that the test preparation had no effect on their scores. Use $\alpha$ = 0.05. Student 1 2 3 4 5 6 7 8 9 Before Score 820 920 810 1180 1060 1100 990 850 1150 After Score 840 920 800 1220 1090 1110 980 890 1170

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 statistics teacher wanted to see whether there was a significant difference in age between day students and night students. A random sample of 35 students from each group was selected. The data are given below. Use the Wilcoxon rank sum test to test the claim that there is no difference in age between the two groups. Use $\alpha =$ .05. Day Students 22 24 24 23 19 19 23 22 18 21 21 18 18 25 29 24 23 22 22 21 20 20 20 27 17 19 18 21 20 23 26 30 24 21 25 Evening Students 18 23 25 23 21 21 23 24 27 31 34 20 20 23 19 25 24 27 23 20 20 21 25 24 23 28 20 19 23 24 20 27 21 29 30

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 telemarketer solicited households to change their long-distance carrier. The results for one afternoon are shown, where C represents the households that changed their carrier and S represents the households that kept their existing carrier. Can you conclude that the sequence of results is random? Use $\alpha$ = 0.05.

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. -Verbal SAT scores for students randomly selected from two different schools are listed below. Use the Wilcoxon rank sum test to test the claim that there is no difference in the scores from the two schools. Use $\alpha$ = 0.05. School 1 School 2 540 510 760 480 430 670 470 740 520 420 700 580 570 770 600 680 540 520 580 720 740 620 630 530

Perform the indicated Kruskall-Wallis 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 researcher wishes to test the claim that there is a difference in the distribution of ages of elementary school, high school, and community college teachers. Teachers are randomly selected from each group. Their ages are recorded below. Can you conclude that the distributions of teachersʹ ages at these different levels of education are different? Use $\alpha = 0.05 \text {. }$ Elementary School Teachers High School Teachers Community College Teachers 28 41 44 33 46 50 32 43 41 57 52 66 42 47 50 30 36 40

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 physician claims that a personʹs diastolic blood pressure can be lowered by listening to a relaxation tape each evening. Ten subjects are randomly selected and their blood pressures are measured. The 10 patients then listen to the tapes each evening for one month. At the end of the month, their blood pressures are measured again. The data (in mm Hg)are listed below. Use the Wilcoxon signed-rank test to test the physicianʹs claim. Use $\alpha =$ .05. Patient 1 2 3 4 5 6 7 8 9 10 Before 83 82 99 86 90 80 91 94 92 81 After 80 76 99 78 84 69 94 84 88 65

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 real estate agent surmises that the median rent for a one-bedroom apartment in a beach community in southern California is at least $1500 per month. The rents for a random sample of 15 one-bedroom apartments are listed below. Test the agentʹs claim. Use $\alpha = 0.01$ \ 1800 \ 1750 \ 1200 \ 1375 \ 1235 \ 2250 \ 1675 \ 1170 \ 1890 \ 2500 \ 1495 \ 1500 \ 1575 \ 1500 \ 1280

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 researcher wants to know if the length of sentences received for a particular type of crime was the same for men and women. The length of sentence received was recorded for a random sample of men and women . The data, in years, are listed below. Use the Wilcoxon rank sum test to test the claim that there is no difference between the sentences received by men and the sentences received by women. Use $\alpha$ = 0.05. Men 6 18 12 14 15 22 Women 5 8 5 10 22 8 Men 10 18 8 15 19 20 Women 30 4 6 9 13 23

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 weight-lifting coach claims that weight-lifters can increase their 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 Wilcoxon signed-rank test to test the claim that the vitamin E supplement is effective in increasing athletesʹ strength. Use $\alpha = 0.05 .$ Athlete 1 2 3 4 5 6 7 8 9 Before 185 241 251 187 216 210 204 219 183 After 195 246 251 185 223 225 209 214 188

The sequence shows a companyʹs daily sales, in thousands of dollars, for the business days during the month of September. Test the claim that the sales are random. 10 10 15 12.5 20 12.5 10 10 12.5 20 8 10 10 20 15 9 12.5 12.5 20 17.5

The table below lists the verbal and math SAT scores of 35 students selected at random. Find the critical values to 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 380 450 475 410 460 425 510 430 300 310 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

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. -Two poker players are dealt cards in the sequence shown, where B represents a black card and R represents a red card. Can you conclude that the dealing of cards was not random? Use $\alpha$ = 0.05. B B B R B R B R R B B B R R

A telemarketer solicited households to change their long-distance carrier. The results for one afternoon are shown, where C represents the households that changed their carrier and S represents the households that kept their same carrier. Find the test statistic G to test for randomness. SC

A club professional at a major golf course claims that the course is so tough that even professional golfers rarely break par of 68. The scores from a random sample of 20 professional golfers are listed below. Find the Critical value to test the club professionalʹs claim. Use $\alpha = 0.05$ 67 65 68 68 71 70 62 74 68 73 65 67 69 69 76 74 68 70 71 61

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 club professional at a major golf course claims that the course is so tough that the median score is greater than 75. The scores from a random sample of 20 professional golfers are listed below. Test the club professionalʹs claim. Use $\alpha = 0.05 \text {. }$ 74 72 75 75 78 77 69 81 75 80 72 74 76 76 83 81 75 77 78 68

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. -In an area of the Midwest, records were kept on the rainfall and the yield of wheat. Can you conclude that there is a correlation between rainfall and yield of wheat? Use $\alpha$ = 0.01. Rainfall (inches) 13.5 11.8 16.4 15.5 21.8 13.3 10.0 18.6 19.0 Yield (bushels per acre) 53.5 49.2 61.8 62.0 85.4 52.2 34.9 79.0 81.8

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. -Nine students took the SAT test. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Use the sign test to test the claim that the test preparation has no effect on their scores. Use $\alpha = 0.05$ Student 1 2 3 4 5 6 7 8 9 Before Score 860 820 910 990 1000 930 870 1180 920 After Score 880 820 900 1030 1030 940 860 1220 940

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 temperatures on randomly chosen days during a summer class and the number of absences from class on those days are listed below. Can you conclude that there is a correlation between temperature and the number absent? Use $\alpha = 0.01$ Temp 75 88 94 93 91 101 78 103 83 Absences 6 10 13 13 11 18 7 18 8