Question

In the journal Mental Retardation, an article reported the results of a peer tutoring program to help mildly mentally retarded children learn to read. In the experiment, 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 n1 = 31 children, the mean score on the vocabulary portion of the test was x1 = 368.4, with sample standard deviation s1 = 38.9. The average score on the vocabulary portion of the test for the n2 = 31 subjects in the control group was x2 = 351.0 with sample standard deviation s2 = 53.1. Use a 5% level of significance to test the claim that the experimental group performed better than the control group.

(a) What is the level of significance? State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 > ?2 H0: ?1 = ?2; H1: ?1 < ?2 H0: ?1 ? ?2; H1: ?1 = ?2 H0: ?1 = ?2; H1: ?1 ? ?2

(b) What sampling distribution will you use?

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

(e) Interpret your conclusion in the context of the application.

Answer 1

Two sample t-test for equal variances:

b) Two sample t-test for equal variances.

df= n1+n2-2= 31+31-2= 60

pooled varinace:

c) P-value: 0.073

d) Fail to reject H0 and the test is not significant at 0.05 significant level.

e) The test statistic is not significant and failed to reject H0. There is insufficient evidence to support the claim that the experimental group performed better than the control group.