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, the mildly retarded children were randomly divided into two groups: the experimental group received peer tutoring along with regular instruction, and the control group received regular instruction with no peer tutoring. There were n₁ = n₂ = 30 children in each group. The Gates–MacGintie Reading Test was given to both groups before instruction began. For the experimental group, the mean score on the vocabulary portion of the test was x̅₁ = 344.5, with sample standard deviation s₁ = 49.1. For the control group, the mean score on the same test was x̅₂ = 354.2, with sample standard deviation s₂ = 50.9. Use a 5% level of signifi­cance to test the hypothesis that there was no difference in the vocabulary scores of the two groups before the instruction began.

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) Check Requirements What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic and corresponding z or t value as appropriate.

(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(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 a?

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

For degrees of freedom d.f. not in the Student’s t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and therefore produce a slightly more “conservative” answer.

Answers may vary due to rounding.