Exam 14: Nonparametric Statistics Available Online

Online classes are becoming more and more prevalent at the college level. A statistics instructor randomly sampled ten students from his traditional face-to-face class and ten students from his Online class to compare their comprehension of the material that was taught in the class. He Administered the same final exam to each student and wants to use the Wilcoxon Rank Sum test to Compare their exam scores. The results are shown below: Calculate the test statistic for the Wilcoxon Rank Sum Test.

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 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 rank test to test the claim that the incentive program cuts down on the number of days missed by teachers. Use $\alpha = .05$ . Teacher 1 2 3 4 5 6 7 8 9 10 Days Absent Before Incentive 8 6 7 3 9 6 2 7 9 4 Days Absent After Incentive 6 5 7 1 8 4 0 8 7 4

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 bearing on weight loss. Use $\alpha = .02$ .

Eight SmartCars were randomly selected and the highway mileage of each was noted. The highway mileage per gallon for each car is shown below: 32 42 29 34 41 37 38 39 40 It was desired to determine if the median miles per gallon of all SmartCars exceeded 35 miles per gallon. Find the p-value when conducting the Sign Test.

Specify the rejection region for the Wilcoxon signed rank test in the following situation. $n = 35 , \alpha = .10$ $H _ { 0 }$ : Two probability distributions, 1 and 2, are identical $H _ { \mathrm { a } }$ : Probability distribution of population 1 is shifted to the right or left of the probability distribution for population 2

The ages and systolic blood pressures (measured in millimeters of mercury)of 9 randomly selected adults are given below. Can you conclude that there is a correlation between age and blood pressure? Use \alpha=.05 . Age 38 41 45 48 51 53 57 61 65 Pressure 116 120 123 131 142 145 148 150 152

The table below lists the verbal and math SAT scores of 10 students selected at random. Test the hypothesis of no correlation between verbal and math SAT scores. Use $\alpha = .05$ . Verbal 475 560 565 470 550 Math 560 630 655 590 640 Verbal 580 480 530 600 490 Math 605 690 610 480 490

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 H-test to test the claim that there is no difference in the distribution of the populations. $\text { Use } \alpha = .05$ Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer 4 13 12 13 10 12 15 10 12 13 12 11 10 14 12 10 11 14 12 9 12 13 13 10 11

The sign test can not be used when an outlier is present.

The Wilcoxon signed rank test for large samples can be used when n ≥ 10.

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 the temperature and the number absent? Use $\alpha = .01$ . Temp 68 81 87 86 84 94 71 96 76 Absences 1 5 8 8 6 13 2 13 3

The advantage of the Friedman $F _ { r }$ -test is that the measurements within each block do not need to be ranked.

A scientist is hoping to compare the levels of DDT toxin found in three species of fish in a local river. He randomly samples 7 of each species to use in the analysis. For each fish, he measures the Amount of DDT toxin present. The data is shown below: Ideally he will be able to determine if a difference exists in the population of DDT toxins found in the three fish species. The test statistic was determined to be $\mathrm { H } = 11.718$ . State the appropriate conclusion when testing at $\alpha = 0.025$ .

A consumer protection organization claims that a new car model gets less than 22 miles per gallon of gas. Ten cars are tested. The results are given below. Test the organization's claim. Use $\alpha = .05$ . 16.8 14.6 20.8 15.9 19 21.2 24.3 18.9 13.7 20

Online classes are becoming more and more prevalent at the college level. A statistics instructor randomly sampled ten students from his traditional face-to-face class and ten students from his Online class to compare their comprehension of the material that was taught in the class. He Administered the same final exam to each student and wants to use the Wilcoxon Rank Sum test to Compare their exam scores. The results are shown below: Calculate the test statistic for the Wilcoxon Rank Sum Test for Large Samples.

For a valid signed rank test, the probability distribution from which the sample of paired differences is drawn must be continuous.

Nonparametric methods focus on the location of the probability distribution, rather than on specific parameters of the population.

A researcher wants to know if the time spent in prison for a particular type of crime is the same for men and women. A random sample of men and women were each asked to give the length of sentence received. The data, in years, are listed below. Use the Wilcoxon rank sum procedure to test the claim that there is no difference in the sentence received by each gender. Use $\alpha = .05$ . Men 5 17 11 13 14 21 Women 4 7 4 9 21 7 Men 9 17 7 14 18 19 Women 29 3 5 8 12 22

Suppose you want to compare two treatments, A and B. In particular, you wish to determine whether the distribution for population B is shifted to the right of the distribution for population A. You plan to use the Wilcoxon rank sum test. a. Specify the null and alternative hypotheses you would test. b. Suppose you obtained the following independent random samples of observations on experimental units subjected to the two treatments. Conduct the test of hypotheses described above, using $\alpha = .05$ . Sample A: 1.2, 1.5, 2.3, 3.2, 3.7, 4.1 Sample B: 2.5, 2.8, 3.6, 4.2, 4.5

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The median distance of the five longest hits using each bat is shown in The table below. The goal is to determine if a difference exists in the population of median Distances for each of the four brands of baseball bat. Batter Brand 1 Brand 2 Brand 3 Brand 4 1 307 315 300 275 2 310 317 305 285 3 335 335 335 302 4 325 328 320 300 5 300 305 295 270 6 345 350 340 310 7 312 315 308 300 8 298 302 295 288 Use the Friedman $\mathrm { F } _ { \mathrm { r } } - \mathrm { Test }$ to calculate the test statistic used to determine if at least two of the distance distributions for the four baseball bats differ in location.