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 = 349.4 with sample standard deviation s2 = 56.4. (a) Use a 1% level of significance to test the claim that the experimental group performed better than the control group. (i) What is the level of significance? 0.01 Correct: Your answer is correct. 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 . (ii) 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? 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 > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot . (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? 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. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (v) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is insufficient 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. 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 sufficient evidence that the mean score for the experimental group is higher than for the control group. (b) Find a 98% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limit Explain the meaning of the confidence interval in the context of the problem. Because the interval contains only positive numbers, this indicates that at the 98% confidence level, the population mean score for the experimental group was higher than for the control group. Because the interval contains both positive and negative numbers, this indicates that at the 98% confidence level, we cannot say that the population mean score for the experimental group was higher than for the control group. Because the interval contains both positive and negative numbers, this indicates that at the 98% confidence level, the population mean score for the experimental group was lower than for the control group. Because the interval contains only negative numbers, this indicates that at the 98% confidence level, the population mean score for the experimental group was lower than for the

Answer 1

Given
X1 bar	368.4	X2 bar	349.4
S1	39.3	S2	56.4
n1	30	n2	30

a)

Hypothesis:

H0: μ1 = μ2; H1: μ1 > μ2

t Critical Value :

tc = 2.3924 (Use t table)

Rejection region:

tstat > tcritical, To reject H0

Test:

Sp^2 = ((n1-1)S1^2+(n2-1)S2^2)/(n1+n2-2) = 2362.725

t stat = (X1 bar-X2 bar )/SQRT(Sp^2*(1/n1 + 1/n2)) = 1.5139

P value:

P value = 0.0677 (use t table)

P value > 0.01, Do not reject H0

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

Conclusion:

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.

b)

98% confidence interval for μ1 − μ2

CI	Equal variance
tc	2.392377475	T.INV.2T(D1,D2)
Upper	49.02552872	(X1 bar-X2 bar )+tc*Sp*SQRT(1/n1 + 1/n2)
Lower	-11.02552872	(X1 bar-X2 bar )-tc*Sp*SQRT(1/n1 + 1/n2)

CI = (-11.0255, 49.0255)

Because the interval contains both positive and negative numbers, this indicates that at the 98% confidence level, we cannot say that the population mean score for the experimental group was higher than for the control group.