Question

Question Help Suppose you want to test a hypothesis that two treatments A and B, are equivalent against the alternative hypothesis that the responses for Atend to be larger than those for B. You plan to use a paired ofference experiment and to analyze the resulting data shown in the accompanying datatable, with the Wilcoxon signed rankos. Complete partea and b. Click the loon to view the datatable Click the leon to view a table of critical values for the Wilcoxon signed rankost a. Specify the null and alterative hypotheses you would test Ho: The probability distribution for treatment is the probability distribution for treatment B. Hy: The probability distribution for treatment is the probability distribution for treatment B. b. Suppose the paired difference experimenteided the data in the given table. Conduct the test of parta, where the differences are (A-B). Test using a 0.06. Find the best statistic for this test. Select the correct choice below and fill in the answer box within your choice (Type an integer or a decimal) O A T.- Data Table OB.T. - OG TE Pair A 1 77 78 Find the rejection region for this best at 0.05. Select the correct choice below and in the answer box within your choice. 2 B0 88 3 49 31 OATS 76 62 53 OB. T. 54 31 OG T.5 5 6 7 B 31 What is the correct conclusion for this hypothesis test? Print Done O A Do not reject Hy. There is sufficient evidence to indicate that the responses for Atend to be larger than those for at 0.05. OB. Reject Ho. There is insuficient evidence to indicate that the responses for Atend to be larger than those for B0.06 Click to select your answer

please help with all parts

Answer 1

Solution:

Now, the following table is obtained by removing the ties and organizing the absolute differences in ascending order: Sample Differen Pair Sample 2 Abs Differen ce Sign 1 ce 1 77 78 -1 1 -1 6 53 54 -1 1 -1 7 54 58 -4 4 -1 8 37 31 6 6 +1 3 59 49 10 10 +1 4 43 31 12 12 +1 5 76 62 14 14 +1 2 80 65 15 15 +1 Now that the absolute differences are in ascending order, we assign ranks to them, taking care of assigning the average rank to values with rank ties (same absolute value difference) Sample Abs. Differen Sample 2 Pair Rank Sign 1 ce 1 77 78 1 1.5 -1 6 53 54 1 1.5 -1 7 54 58 4 3 -1 8 37 31 6 4 +1 3 59 49 10 5 +1 4 43 31 12 6 +1 5 76 62 14 7 +1 2 80 65 15 8 +1 The sum of positive ranks is: W+ = 4+ 5+ 6+ 7+ 8 = 30 and the sum of negative ranks is: W = 1.5 +1.5+3= 6 Hence, the test statistic is T = min{W+,W-} = min{30,6} = 6. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: Median (Difference) = 0 H: Median (Difference) #0

(2) Rejection Region The critical value for the signficance level a = 0.05 provided, and the type of tail specified is T* = 3, and the null hypothesis is rejected if T <3. (3) Decision about the null hypothesis Since in this case T = 6 >3, there is not enough evidence to claim that the population median of differences is different than 0, at the a = 0.05 significance level.