Question

A random sample of 9 college freshmen underwent an intensive training course to improve their biology test scores. Each student’s test scores from before the course and after the course are listed below. Calculate a two-sided 95% confidence interval for the mean difference in the scores. Give an interpretation of the confidence interval. You MUST show all your work to receive full credit. Partial credit is available.

Student	Before	After
1	60	74
2	55	71
3	68	72
4	49	65
5	61	77
6	79	80
7	72	79
8	59	82
9	74	84

Answer 1

From the given data, values of d = Before - After is calculated as follows:

Student	Before	After	d = After - Before
1	60	74	14
2	55	71	16
3	68	72	4
4	49	65	16
5	61	77	16
6	79	80	1
7	72	79	7
8	59	82	23
9	74	84	10

From d values, the following Table is calculated:

n = 9

= 107/9 = 11.8889

d	d -	(d - )2
14	2.1111	4.4568
16	4.1111	16.9012
4	-7.8889	62.2346
16	4.1111	16.9012
16	4.1111	16.9012
1	-10.8889	118.5879
7	-4.8889	23.9012
23	11.1111	123.4568
10	-1.8889	3.5679
Total		386.8889

Standard Deviation is given by:

s_d = 6.9542

SE = s_d/

= 6.9542/

= 2.3181

= 0.05

ndf = 9 - 1 = 8

From Table, critical values of t = 2.3060

Confidence Interval:

11.8889 (2.3060 X 2.3181)

= 11.8889 5.3455

= (6.5434 ,17.2344)

Confidence Interval:

6.5434 < <   17.2344