Question

Problem 3. (30pts) Two methods for teaching reading were applied to two randomly selected groups of elementary school children and then compared on the basis of a reading comprehension test given at the end of the learning period. The sample means and variances computed from the test scores are shown in the accompanying table. Method I Number of children in group11 64 52 Method II 14 69 71 Do the data present sufficient evidence to indicate a difference in the mean scores for the populations associated with the two teaching methods. Report your results using the rejection region (15pts) and the p-value (15pts) method.

Answer 1

To Test :-

H0 :-   $\mu_{1} = \mu_{2}$

H1 :-   $\mu_{1} \neq \mu_{2}$

Test Statistic :-
$t = (\bar{X_{1}} - \bar{X_{2}}) / \sqrt{ ( S_{1}^{2} / n1) + (S_{2}^{2} / n2)}$
$t = ( 64 - 69 ) / \sqrt{ ( 7.2111^{2} / 11) + ( 8.4262^{2} / 14)}$
t = -1.5973

Test Criteria :-
Reject null hypothesis if $| t | > t_{\alpha /2, DF}$


DF = 22
$t_{\alpha /2, DF} = t_{ 0.05 /2, 22 } = 2.074$
$| t | > t_{\alpha /2, DF} = 1.5973 < 2.074$
Result :- Fail to Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 1.5973 ) = 0.1245
Reject null hypothesis if P value < $\alpha = 0.05$ level of significance
P - value = 0.1245 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- We Accept H0

There is insufficient evidence to support the claim that there is a difference in the mean score for the population associated with the two teaching methods at 5% level of significance.