Question

The developer of a phonetics game claims that use of the game will improve the reading scores by at least 10 points in 2nd grade children.  The reading levels of eight randomly selected second grade children were tested before use of the game and then retested after exposure to the game for six months.  Using a 5% significance level, is there statistically sufficient evidence to support the claim that the post test scores were higher than the pretest scores?  Perform an appropriate hypothesis test showing necessary statistical evidence to support your final given conclusion.

PreTest	Post Test
70	75
65	70
85	90
50	70
75	90
80	80
90	95
60	70

Answer 1

Pre Test	Post Test	Difference(d)
70	75	-5
65	70	-5
85	90	-5
50	70	-20
75	90	-15
80	80	0
90	95	-5
60	70	-10
	Total	-65

Claim: the post-test scores were higher than the pretest scores.

The null and alternative hypothesis is

Level of significance = 0.05

Sample size = n = 8

Sample mean of difference = = - 8.125

Sample standard deviation of difference = = 6.5124

Test statistic is

Degrees of freedom = n - 1 = 8 - 1 = 7

Critical value = 1.895    ( Using t table)

Test statistic | t | > critical value we reject null hypothesis.

Conclusion:

The post-test scores were higher than the pretest scores.