Question

Athlete	Before	After
1	220	206
2	181	179
3	210	218
4	231	235
5	201	203

A special vitamin which claims to increase muscle strength is tested on 5 weight lifters. Athletes are selected and the weight they can bench press is recorded before and then after two weeks of taking the vitamin.

2. Estimate mean difference in weight lifted before/after vitamin, and then calculate a standard error for your estimate.

Answer 1

Athelete	x(before)	y (after)	d=x-y	d^2
1	220	206	14	196
2	181	179	2	4
3	210	218	-8	64
4	231	235	-4	16
5	201	203	-2	4
Total			2	284

n=5 , sum(d) = 2 , sum(d^2) = 284

E(d) = mean difference in weight = sum(d) / n

= 2 / 5

= 0.4

E(d^2) = sum(d^2) / n = 284 /5 = 56.8

var(d) = E(d^2) - (E(d) ) ^ 2

= 56.8 - (0.4) ^ 2

= 56.8 - 0.16

= 56.64

std deviation(d) = square root of variance = sqrt(56.64) = 7.53

Standard error =SE = standard deviation(d) / sqrt(n)

= 7.53 / sqrt(5)

= 7.53 / 2.24

= 3.37

Answer:- mean = 0.4 & standard error = 3.37