Question

To test the effect of a physical-fitness course on one’s physical ability, the number of sit-ups that a person could do in 1 minute, both before and after the course, was recorded. Six randomly selected participants scored as shown below. Can we conclude that a significant amount of improvement took place? Use α = 0.01 and assume normality. (Please show all steps of classical approach.)

Before 29 22 25 29 26 24

After 30 26 25 35 33 36

Answer 1

Step 1:

Ho : = 0

Ha: < 0 (Claim)

= Before - after (i.e. there is improvement after the course)

Step 2: Paired t test

employee	Before	After	Diff (Bef-after)	Dev (diff - mean)	Sq deviation
1	29.0	30.0	-1.0	4.00	16.00
2	22.0	26.0	-4.0	1.00	1.00
3	25.0	25.0	0.0	5.00	25.00
4	29.0	35.0	-6.0	-1.00	1.00
5	26.0	33.0	-7.0	-2.00	4.00
6	24.0	36.0	-12.0	-7.00	49.00
Total	155	185	-30.000	0.0000	96.0000

= -30 / 6 = -5

SD for the diff

p value = TDIST(2.795, 5,1) = 0.0191

Step 3:

t critical for left tailed test: - 3.364930

As the t stat does not fall in the rejection area, we fail to reject the Null hypothesis.

Also p value is greater than alpah (0.01) hence we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that significant improvement took place after the course.