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 = 30 children, the mean score on the vocabulary portion of the test was x₁ = 368.4, with sample standard deviation s₁ = 39.3. The average score on the vocabulary portion of the test for the n₂ = 30 subjects in the control group was x₂ = 349.0 with sample standard deviation s₂ = 56.2. Use a 1% 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: μ₁ = μ₂; H₁: μ₁ ≠ μ₂

H₀: μ₁ ≠ μ₂; H₁: μ₁ = μ₂     

H₀: μ₁ = μ₂; H₁: μ₁ > μ₂

H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

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

The standard normal. Both sample sizes are large with known standard deviations.

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

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

The standard normal. Both sample sizes are large with unknown standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)


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

P-value > 0.250

0.125 < P-value < 0.250     

0.050 < P-value < 0.1250.

025 < P-value < 0.0500

.005 < P-value < 0.025

P-value < 0.005

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 α?

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.     

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

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

Fail to reject the null hypothesis, there is insufficient evidence that the mean score for the experimental group is higher than for the control group.

Reject the null hypothesis, there is insufficient evidence that the mean score for the experimental group is higher than for the control group.     

Reject the null hypothesis, there is sufficient evidence that the mean score for the experimental group is higher than for the control group.

Fail to reject the null hypothesis, there is sufficient evidence that the mean score for the experimental group is higher than for the control group.

Answer 1