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, 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 x₁ = 344.5, with sample standard deviation s₁ = 49.9. For the control group, the mean score on the same test was x₂ = 354.2, with sample standard deviation s₂ = 50.5.

(a) 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.

(i) What is the level of significance?

0.05

State the null and alternate hypotheses.

H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂     

(ii) What sampling distribution will you use? What assumptions are you making?

The Student's t. Both sample sizes are large with unknown standard deviations.

What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)

(iii) Find (or estimate) the P-value.

P-value > 0.500

0.250 < P-value < 0.500

0.100 < P-value < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

[I need assistance in finding the value of the sample test statistic, as well as finding (or estimating) the P-value.]

Answer 1