Exam 15: Nonparametric Statistics

Provide an appropriate response. -The table below lists the amounts (in dollars) spent on clothing and entertainment over the last year by 10 adults selected at random. Find the critical values to test the hypothesis of no correlation between spending in these two areas. Use $\alpha = 0.05$ . Clothing 315 400 405 310 390 Entertainment 400 470 495 430 480 Clothing 420 320 370 440 330 Entertainment 445 530 450 320 330

Write the word or phrase that best completes each 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 E, they are tested again. The new results are listed below. Use the Wilcoxon signed-ranks test 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 206 185 207 182 266 228 242 217 225 After 216 190 207 180 273 243 247 212 230

Provide an appropriate response. -Which of the below is an advantage of nonparametric statistical procedures

Choose the one alternative that best completes the statement or answers the question. -In order to be able to use the Mann-Whitney Test, the distributions must have the same shape.

Write the word or phrase that best completes each statement or answers the question. -Test the hypothesis that the median age of art teachers is less than 45 years. A random sample of 60 art teachers found 25 above 45 years, 33 below 45 years, and the rest exactly 45 years. Use $\alpha = 0.01$ .

Write the word or phrase that best completes each statement or answers the question. -In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of soybeans (bushels per acre). Can you conclude that there is a correlation between rainfall and yield per acre? Use $\alpha = 0.01$ . Rainfall 12.0 10.3 14.9 14.0 20.3 11.8 8.5 17.1 17.5 Yield 52.0 47.7 60.3 60.5 83.9 50.7 33.4 77.5 80.3

Choose the one alternative that best completes the statement or answers the question. -A government agency believes that the median hourly wages for retail store workers in the central U.S. is $\$ 6.70$ . In a random sample of 100 workers, 68 were paid less than $\$ 6.70,10$ were paid $\$ 6.70$ , and the rest more than $\$$ 6.70. Find the critical values to test the government's hypothesis. Use $\alpha = 0.05$ .

Write the word or phrase that best completes each statement or answers the question. -The number of absences and the final grades of 9 randomly selected students from a French class are given below. Can you conclude that there is a negative correlation between the final grade and the number of absences? Use $\alpha = 0.01$ . Number of Absences 0 3 6 4 9 2 15 8 5 Final Grade 98 86 80 82 71 92 55 76 82

Provide an appropriate response. -Use the Wilcoxon matched-pairs signed-ranks test to test the given hypothesis at the $\alpha = 0.05$ level of significance. The dependent samples were obtained randomly. Hypotheses: $\mathrm { H } _ { 0 } : \mathrm { M } _ { \mathrm { D } } = 0$ versus $\mathrm { H } _ { 1 } : \mathrm { M } _ { \mathrm { D } } < 0$ with $\mathrm { n } = 30$ , and $\mathrm { T } _ { + } = 193$

Write the word or phrase that best completes each statement or answers the question. -The final exam scores of 10 randomly selected algebra students and the number of hours they studied for the exam are given below. Can you conclude that there is a positive correlation between the scores on the test and the times spend studying? Use $\alpha = 0.01$ . Hours 7 9 6 12 6 8 8 9 10 7 Scores 69 84 64 92 70 82 89 94 94 75

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 critical value $\chi ^ { 2 }$ to test the hypothesis that there is no difference in the distribution of the populations. Use $\alpha = 0.05$ . Schedule 1 Schedule2 Schedule 3 Schedule 4 10 9 10 7 9 12 7 9 10 9 8 7 11 9 7 8 11 9 6 9 10 10 7 8

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 critical values to test the hypothesis of no correlation between the rankings. Use $\alpha = 0.05$ . 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 owner of a major golf course believes that the course is so tough that most golfers rarely break par of $74 .$ The scores from a random sample of 20 golfers are listed below. Test the club owner's hypothesis. Use $\alpha = 0.05$ . 73 71 74 74 77 76 68 80 74 79 71 73 75 75 82 80 74 76 77 67

Write the word or phrase that best completes each statement or answers the question. -A real estate agent surmises that the median rent for a studio apartment in a mountain community in Colorado is less than $\$ 1400$ per month. The rents for a random sample of 15 studio apartments are listed below. Test the agent's hypothesis. Use $\alpha = 0.01$ . \ 1700 \ 1650 \ 1100 \ 1275 \ 1135 \ 2150 \ 1575 \ 1070 \ 1790 \ 2400 \ 1395 \ 1400 \ 1475 \ 1400 \ 1180

Choose the one alternative that best completes the statement or answers the question. -A college dean believes that the median hours spent studying by full time students is at least 12 hours per week. In a random sample of 100 students, 65 studied more than 12 hours, 10 studied exactly 12 hours and the rest studied less than 12 hours. Find the critical value to test the dean's hypothesis. Use $\alpha = 0.05$ .

Choose the one alternative that best completes the statement or answers the question. -Spearman's rank-correlation test is used to test hypotheses regarding________

Choose the one alternative that best completes the 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 find the test statistic T 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 1200 810 1090 1070 1080 990 800 1100 820 After Score 1220 810 1080 1110 1110 1000 790 1140 840

Write the word or phrase that best completes each statement or answers the question. -In a study of the effectiveness of dietary restrictions on weight loss, 20 people were randomly selected to participate in a program for 30 days. Use the Wilcoxon signed -ranks test to test the hypothesis that dietary restrictions have no bearing on weight loss. Use $\alpha = 0.02$ .

Provide an appropriate response. -A soda machine is set to fill bottles with 24 ounces of cola. As part of a quality control program, an inspector records the amount of fill over or under 24 ounces for one minute. His observations are shown below. -0.40 -0.45 -0.21 -0.15 -0.71 -0.05 -0.84 -0.12 -0.05 -0.58 -0.97 -1.01 -0.75 0.50 0.08 -0.45 -0.27 -0.75 -0.07 -1.00 0.25 0.25 0.91 0.99 0.36 0.05 0.11 0.31 0.84 0.67 0.45 0.60 0.01 0.98 0.22 0.72 0.77 0.48 0.13 0.39 -0.73 -0.78 -0.90 -0.14 -0.68 0.80 0.12 0.16 0.37 0.27 Is there evidence at the $\alpha = 0.01$ level of significance to support the hypothesis that the filling process is not random with respect to amounts over and under 24 ounces?

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 test statistic H to test the hypothesis that there is no difference in the distribution of the populations. Use $\alpha = 0.05$ .