Stratford University MTh 310 Module 11 Provide an appropriate response. 1) Describe parametric and nonparametric tests. Explain why nonparametric tests are important. 2) ___________________ statistical processes are often called distribution free procedures. Use the sign test to test the indicated claim. 3) Fourteen people rated two brands of soda on a scale of 1 to 5. At the 5 percent level, test the null hypothesis that the two brands of soda are equally popular. Use the sign test to test the given alternative hypothesis at the α = 0.05 level of significance. 4) Alternative Hypothesis: the median is more than 55. An analysis of the data reveals that there are 5 minus signs and 14 plus signs. Provide an appropriate response. 5) A convenience store owner believes that the median number of newspapers sold per day is 54. A random sample of 20 days yields the data below. Find the test statistic x to test the owner's hypothesis. Use α = 0.05. 37 53 64 69 36 60 75 32 38 43 52 59 59 49 49 54 54 64 59 43 6) What is the test statistic, k, if we have a small sample size and the alternative hypothesis of a one-sample sign test is H1 : M < M0? 7) 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 α = 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 Draw a scatter diagram for the given data, compute Spearman's rank correlation coefficient rs, and determine if X and Y are associated at the α = 0.05 level of significance. 8) X 1 2 3 6 6 8 Y 1.2 3.7 5.1 5.8 6.2 6.5 1 Use the Mann–Whitney test to test the given hypotheses at the α = 0.05 level of significance. The independent samples were obtained randomly. 9) Hypotheses: H0: Mx = My versus H1: Mx ≠ My with n1= 24, n2 = 21, and S = 760. Provide an appropriate response. 10) Use the Wilcoxon matched-pairs signed-ranks test to test the given hypothesis at the α = 0.05 level of significance. The dependent samples were obtained randomly. Hypotheses: H0: MD = 0 versus H1: MD ≠ 0 with n = 45, T+ = 189, and T- = 846 11) The nonparametric test used in place of the one-way ANOVA is the . 12) 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 α = 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 2 Answer Key Testname: MTH310_MODULE11 1) Parametric tests require assumptions about the nature or shape of the populations involved. Most of the tests we have worked with have required that the populations be normal. Nonparametric tests do not have requirements as to parent population. 2) Nonparametric 3) H0: The two brands of soda are equally popular. H1: The two brands of soda are not equally popular. Test statistic: x = 3. Critical value: x = 2. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two brands are equally popular. 4) H0: M = 55 versus H1: M > 55; k = 5; critical value: 5. Reject H0. 5) 8 6) k is the number of + signs 7) critical value 40; test statistic T = 42.5; fail to reject H0; There is not sufficient evidence to reject the hypothesis. 8) y 6 5 4 3 2 1 1 2 3 4 5 6 7 8 x rs = 0.986; H0: X and Y are not associated versus H0: X and Y are associated. Critical values: -0.886 and 0.886; reject H0. 9) T = 460; z0 = 4.73, -z0.025 = -1.96, z0.025 = 1.96; Reject H0. 10) z = -3.71; |z| > z0.025 = 1.96; reject H0; There is sufficient evidence that the medians are different. 11) Kruskal-Wallis test 12) critical value 5.991; test statistic H ≈ 10.187; reject H0; The data provide ample evidence that there is a difference in the distribution of the populations. 3