In the article cited in Problem 17, the results of the following experiment were reported: Form 2 of the Gates-MacGintie Reading Test was administered to both an experimental group and a control group after 6 weeks of instruction during which the experimental group received peer tutoring and the control group did not. For the experimental group with n1 = 30 children, the mean score on the vocabulary portion of the test was 1 = 368.4 with sample standard deviation s1 = 39.5. The average score on the vocabulary portion of the test for the n2 = 30 subjects in the control group was 2 = 349.2, with sample standard deviation s2 = 56.6.
(a) Use a 1% level of significance to test the claim that the experimental group performed better than the control group.
(b) Find a 98% confidence interval for μ1 - μ2. Explain the meaning of the confidence interval in the context of the problem.
Please provide the following information for problem part (a):
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) Based on your answers in parts (i) – (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(v) Interpret your conclusion in the context of the application.