Question

1. Nine students took the SAT test. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Use the Sign test to test the claim that the test preparation has no effect on their scores. Use α = 0.05. Student 1 2 3 4 5 6 7 8 9 Before 860 820 910 990 1000 930 870 1180 920 After 880 820 900 1030 1030 940 860 1220 940

2. A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and randomly assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a special diet. At the end of six weeks, the reduction in each subject's blood pressure is recorded. Use the Kruskal-Wallis test to test the claim that there is no difference in the distributions of the blood pressures of the three populations. Use α = 0.05. Group 1 Group 2 Group 3 13 14 11 17 15 10 10 7 4 5 6 2 8 14 6 10 11 6

1. Identify why you choose to perform the statistical test (Sign test, Wilcoxon test, Kruskal-Wallis test).
2. Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.
3. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
4. Find the critical value(s) and identify the rejection region(s).
5. Find the appropriate standardized test statistic. If convenient, use technology.
6. Decide whether to reject or fail to reject the null hypothesis.
7. Interpret the decision in the context of the original claim.

Answer 1

1. Identify why you choose to perform the statistical test (Sign test, Wilcoxon test, Kruskal-Wallis test).
signed test

2. H0: The test preparation has not effect on their scores
H1: The test preparation has effect on their scores

3. Left tailed test

4) Reject H0 if P-value < alpha 0.05

5) From the given data

S.No.	X	Y	Diff = X-Y
1	860	880	-20
2	820	820	0
3	910	900	10
4	990	1030	-40
5	1000	1030	-30
6	930	940	-10
7	870	860	10
8	1180	1220	-40
9	920	940	-20

5) s* = Number of positve signs = 2 Number of samples n = 8 P= P(X 5.*) = P(x2) 8-X = )) ( - )" using Binomial distribution = 0.1445 6) Here P-value is > 0.05, we accept the null hypothesis.

7) Thus we conclude that The test preparation has no effect on their scores