Exam 15: Nonparametric Statistics

Choose the one alternative that best completes the statement or answers the question. -The history department at a college asked its professors and students to rank 8 guest speakers according to their communication skills. The data are listed below. A 10 is the highest ranking and a 1 the lowest ranking. Find the test statistic to test the hypothesis of no correlation between the rankings. Use $\alpha = 0.05 \text {. }$ Speaker 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

Write the word or phrase that best completes each statement or answers the question. -The maximum summer temperatures for nine randomly selected cities (in ${ } ^ { \circ } \mathrm { F }$ ) and the number of summer power outages in those cities are listed below. Can you conclude that there is a correlation between the maximum temperatures and the number of power outages? Use $\alpha = 0.01$ . Temp 74 87 93 92 90 100 77 102 82 Outages 5 9 12 12 10 17 6 17 7

Provide an appropriate response. -Wanting to enjoy the beautiful weather, Cassie took a walk with no destination in mind. At each four-way intersection, she randomly decided to head either north or east. A summary of her walk is shown below. Is there evidence at the $\alpha = 0.05$ level of significance to support the hypothesis that Cassie's walk was not random?

Choose the one alternative that best completes the statement or answers the question. -A football coach believes that a player 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. The results are listed below. Thirty days later, after regular training supplemented by vitamin $\mathrm { E }$ , they are tested again. The new results are listed below. Use the Wilcoxon signed-ranks test to find the critical value to test the hypothesis that the vitamin E supplement is effective in increasing the athletes' strength. Use $\alpha = 0.05$ . Athlete 1 2 3 4 5 6 7 8 9 Before 182 228 195 246 276 242 203 217 274 After 192 233 195 244 283 257 208 212 279

Write the word or phrase that best completes each statement or answers the question. -A realtor wishes to compare the annual property taxes (in dollars) of houses in 4 different cities, all of which are priced approximately the same. The data are listed below. Use the Kruskal-Wallis test to test the hypothesis that there is no difference in the distribution of the populations. Use $\alpha = 0.05$ . City 1 City 2 City 3 City 4 2160 1790 1540 2410 1990 1550 1680 2360 2010 1700 1590 2610 2220 1660 1610 2160 1910 1710 1510 2010 2060 1760 2210 1660 2360 2260

Choose the one alternative that best completes the statement or answers the question. -A physician believes that a person's diastolic blood pressure can be lowered, if, instead of taking a drug, the person performs yoga exercises each evening. Ten subjects are randomly selected. Their blood pressures, measured in millimeters of mercury, are listed below. The 10 patients are instructed in several yoga exercises and told to perform them each evening for one month. At the end of the month, their blood pressures are taken again. The data are listed below. Use the Wilcoxon signed-ranks test to find the critical value to test the physician's hypothesis. Use $\alpha = 0.05$ . Patient 1 2 3 4 5 6 7 8 9 10 Before 92 93 91 96 99 80 85 90 87 94 After 89 87 91 88 93 69 88 80 83 78 A) 8 B) 6 C) 2 D) 4

Choose the one alternative that best completes the statement or answers the question. -The nonparametric test used in place of the one-way ANOVA is the______

Write the word or phrase that best completes each statement or answers the question. -A medical researcher wishes to try three different techniques to lower the weight of obese patients. 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 subject's weight (in pounds) is recorded. Use the Kruskal-Wallis test to test the hypothesis that there is no difference in the distribution of the 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

Provide an appropriate response. -A math teacher wanted to see whether there was a significant difference in commute time between day students and night students. A random sample of 35 students from each group was selected. The data (in minutes) are given below. Test the hypothesis that the median commute time of day students is different than the median commute time of evening students. Use $\alpha = 0.05$ .

Provide an appropriate response. -A runs test for randomness is a test to determine if the data________

Write the word or phrase that best completes each statement or answers the question. -A local company is concerned about the number of days missed by its employees due to illness. A random sample of 10 employees is selected. The numbers of days absent in one year is listed below. An incentive program is offered in an attempt to decrease the number of days absent. The number of days absent in one year after the incentive program is listed below. Use the Wilcoxon signed-ranks test to test the hypothesis that the incentive program cuts down on the number of days missed by employees. Use $\alpha = 0.05$ .

Write the word or phrase that best completes each statement or answers the question. -Nine students took a standardized test. Their scores are listed below. Later on, they took a test preparation course and retook the test. Their new scores are listed below. Use the Wilcoxon signed-ranks test to test the hypothesis 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 900 1170 880 1040 1050 960 1070 1140 980 After Score 920 1170 870 1080 1080 970 1060 1180 1000

Write the word or phrase that best completes each statement or answers the question. -A college dean believes that the median hours spent studying by full time students is at least 14 hours per week. In a random sample of 100 students, 62 studied more than 14 hours, 10 studied exactly 14 hours and the rest studied less than 14 hours. Test the researcher's hypothesis. Use $\alpha = 0.05$ .

Choose the one alternative that best completes the statement or answers the question. -Four different watering schedules are used on bean plants. The number of beans on each randomly selected plant is given below. Use the Kruskal-Wallis test to find the test statistic H to test the hypothesis that there is no difference in the distribution of the populations. Use $\alpha = 0.05$ . Schedule 1 Schedule 2 Schedule 3 Schedule 4 9 8 9 6 8 11 6 8 9 8 7 6 10 8 6 7 10 8 5 8 9 9 6 7

Write the word or phrase that best completes each statement or answers the question. -A labor organization believes that the monthly earnings of landscaping workers are less than $\$ 926$ . To test this, 100 workers are randomly selected and asked to provide their monthly earnings. The data is shown below. Test the labor organization's hypothesis. Use $\alpha = 0.05$ . Weekly Earnings Number of Workers More than \ 926 41 \ 926 5 Less than \ 926 54

Provide an appropriate response. -A medical researcher wishes to try three different techniques to lower the weight of obese patients. 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 subject's weight (in pounds) is recorded. Use the Kruskal-Wallis test to find the critical value to test the hypothesis that there is no difference in the distribution of the populations. Use $\alpha = 0.05$ . Group 1 Group 2 Group 3 16 13 11 17 10 17 14 7 9 20 8 13 18 9 14 13 5 9

Provide an appropriate response. -The Kruskal-Wallis test is the nonparametric version of the parametric _________.

Provide an appropriate response. -A convenience store owner believes that the median number of newspapers sold per day is 79 . A random sample of 20 days yields the data below. Find the test statistic $x$ to test the owner's hypothesis. Use $\alpha = 0.05$ . 62 78 89 94 61 85 100 57 63 68 77 84 84 74 74 79 79 89 84 68

Write the word or phrase that best completes each statement or answers the question. -A consumer advocacy group believes a car manufacturer is falsely advertising that its new model car still gets at least 21 miles per gallon of gas. The advocacy group believes the median miles per gallon is less than 21 . Ten cars are tested. The results are given below. Test the group's hypothesis. Use $\alpha = 0.05$ . 15.8 13.6 19.8 14.9 18 20.2 23.3 17.9 12.7 19

Provide an appropriate response. -Test the hypothesis at the $\alpha = 0.05$ level of significance that the sequence is not random. A A B B B A B A A A A B