Exam 11: Nonparametric Tests Online and CD Only

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 realtor wishes to compare the square footage of houses of similar prices in 4 different cities. The data are listed below. Use the Kruskal-Wallis test to test the claim that there is a difference in the distributions of the square footages in the 4 different cities. Use $\alpha = 0.05 \text {. }$ City 1 City 2 City 3 City 4 2150 1780 1530 2400 1980 1540 1670 2350 2000 1690 1580 2600 2210 1650 1600 2150 1900 1700 1500 2000 2050 1750 2200 1650 2350 2250

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 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 listed below. An incentive program is offered in an attempt to decrease the number of days absent. The numbers of absences in the year after the incentive program are also listed. Use the sign test to test the claim that the incentive program reduces the number of days missed by teachers. Use $\alpha$ = 0.05. Teacher Days Absent Before Incentive Days Absent After Incentive 1 2 3 4 5 6 7 8 9 10 4 7 0 10 8 6 0 3 7 5 3 6 0 8 7 4 1 2 5 5

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 table below lists the verbal and math SAT scores of 10 students selected at random. Test the claim that there is no correlation between verbal and math SAT scores. Use $\alpha$ = 0.05. Verbal 295 380 385 290 370 Math 380 450 475 410 460 Verbal 400 300 350 420 310 Math 425 510 430 300 310

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 medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and randomly assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a special diet. At the end of six weeks, the reduction in each subjectʹs blood pressure is recorded. Use the Kruskal-Wallis test to test the claim that there is no difference in the distributions of the blood pressures of the three populations. Use $\alpha = 0.05$ Group 1 Group 2 Group 3 13 10 8 14 7 14 11 4 6 17 5 10 15 6 11 10 2 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 $1300 per month. The rents for a random sample of 15 one-bedroom apartments Are listed below. Find the critical value to test the agentʹs claim. Use $\alpha = 0.01$ . \ 1600 \ 1550 \ 1000 \ 1175 \ 1035 \ 2050 \ 1475 \ 970 \ 1690 \ 2300 \ 1295 \ 1300 \ 1375 \ 1300 \ 1080

Two poker players are dealt cards in the sequence shown, where B represents a black card and R represents a red card. Find the test statistic G to test for randomness.

The table below lists the verbal and math SAT scores of 10 students selected at random. Find the critical value to test the claim of no correlation between verbal and math SAT scores. Use $\alpha = 0.05 .$ Verbal 495 580 585 490 570 Math 580 650 675 610 660 Verbal 600 500 550 620 510 Math 625 710 630 500 510

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. -An airport security officer searched carry-on bags of people boarding a plane in the sequence shown, where S represents a searched bag and N represents a bag not searched. Can you conclude that the officer conducted a random search? Use $\alpha$ = 0.05.

The sequence shows a companyʹs daily sales, in thousands of dollars, for the business days during the month of September. Find the standardized test statistic, G, to test for randomness. 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

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. -In a study of the effectiveness of physical exercise in weight loss, 20 people were randomly selected to participate in a program for 30 days. Use the sign 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

Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Use the Kruskal-Wallis test to find the critical value H to test the claim that there Is no difference in the distribution of the populations. Use $\alpha$ = 0.05. Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer 4 11 10 11 8 10 13 8 10 11 10 9 8 12 10 8 9 12 10 7 10 11 11 8 9

Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Test the claim using (a)a Kurskal-Wallis test and (b)a one-way ANOVA test that the type of fertilizer makes no difference in the mean number of raspberries per plant. Compare the results. Use $\alpha = 0.01 .$ Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer 4 6 5 6 3 5 8 3 5 6 5 4 3 7 5 3 4 7 5 2 5 6 6 3 4

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 physicianʹs group 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 are given the tapes and told to listen to them each evening for one month. At the end of the month, their blood pressures are measured again. The blood pressures in mm Hg are listed below. Use the sign test to test the physicianʹs claim. Use $\alpha = 0.01$ Patient 1 2 3 4 5 6 7 8 9 10 Before 85 96 92 83 80 91 79 98 93 96 After 82 90 92 75 74 80 82 88 89 80

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 convenience store owner believes that the median number of lottery tickets sold per day is 44. A random sample of 20 days yields the data below. Test the ownerʹs claim. Use $\alpha = 0.05$ 27 43 54 59 26 50 65 22 28 33 42 49 49 39 39 44 44 54 49 33

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 company claims that the median monthly earnings of its farm workers is greater than $919. To test the claim, 100 workers are randomly selected and asked to provide their monthly earnings. The data is shown below. Test the companyʹs claim. Use $\alpha = 0.05$ Weekly Earnings Number of Workers Less than \ 919 44 \ 919 5 More than \ 919 51

A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and assigned to one of three groups. Group 1 is given Medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six Weeks, the reduction in each subjectʹs blood pressure is recorded. Use the Kruskal-Wallis test to find the test Statistic H to test the claim that there is no difference in the distribution of the populations. Group 1 Group 2 Group 3 13 10 8 14 7 14 11 4 6 17 5 10 15 6 11 10 2 6

Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Use the Kruskal-Wallis test to find the test statistic H to test the claim that there Is no difference in the distribution of the populations. Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer 4 11 10 11 8 10 13 8 10 11 10 9 8 12 10 8 9 12 10 7 10 11 11 8 9

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 car dealer claims that its new model car still gets at least 21 miles per gallon of gas. Ten cars are tested. The results are given below. Test the dealerʹs claim. Use $\alpha = 0.05$ 15.8 13.6 19.8 14.9 18 20.2 23.3 17.9 12.7 19

The table below lists the verbal and math SAT scores of 35 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 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 convenience store owner believes that the median number of lottery tickets sold per day is 73. A random sample of 20 days yields the data below. Find the test statistic x to test the ownerʹs claim. 56 72 83 88 55 79 94 51 57 62 71 78 78 68 68 73 73 83 78 62