Question

Stats I, Item # Q-02

At the Joseph Biden Middle School in Down-the-Shore, Delaware, student reading comprehension was evaluated, both pre-test and post-test, bookending a pilot program intervention advocated by the district superintendent and board of education.

Pre-Test	66	45	70	32	60	84	25	76	50	88	75	64
Post-Test	80	54	78	28	76	76	50	72	75	90	75	56

The vice-principal optimistically expected that the intervention would improve reading comprehension scores, whereas the principal pessimistically anticipated that the instrument confused students and scores dropped. Identify the mean average scores on the pre-test and post test instruments, and what the average change was across all participants reported in this sample. Test with 90% confidence that the claim that the intervention had an impact of some kind. State the hypotheses and the conclusions, both technically and contextually. Confirm the findings with the corresponding p-value and confidence interval.

Answer 1

Number	Pre Test	post Test	Difference
	66	80	-14	60.0625
	45	54	-9	7.5625
	70	78	-8	3.0625
	32	28	4	105.0625
	60	76	-16	95.0625
	84	76	8	203.0625
	25	50	-25	351.5625
	76	72	4	105.0625
	50	75	-25	351.5625
	88	90	-2	18.0625
	75	75	0	39.0625
	64	56	8	203.0625
Total	735	810	-75	1542.25

To Test :-

H0 :-  

H1 :-  

Test Statistic :-





t = -1.8285

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Confidence Interval :-



Lower Limit =
Lower Limit = -12.3887
Upper Limit =
Upper Limit = -0.1113
90% Confidence interval is ( -12.3887 , -0.1113 )

P value = P ( t > -1.8285 ) = 0.0947

Decision based on P value

Reject null hypothesis if P value < = 0.10 level of significance

P value = 0.0947 < 0.10, hence we reject null hypothesis

Conclusion :- Reject H0

There is sufficient evidence to support the claim that the intervention had an impact of some kind.