Question

Consider the following information.

Standard Deviation

Mean Observed Time

Work Element	(minutes)	(minutes)	Performance Rating
1	0.8	8.2	1.3
2	0.6	9.2	1.1
3	0.5	4.4	0.8

Determine the sample size needed if the standard time estimate is to be within 5% of the true mean 99% of the time.

Answer 1

Answer: - Given data

Standard deviation of work elements and mean observed time

Formula to calculate the sample size needed

N = [(z/a)*(s/x-bar)]²

Where z = 2.58 for 99% confidence interval, a = desired accuracy = 0.05

S = standard deviation and x-bar = mean observed time

For workelement 1 = [(2.58/0.05)*(0.8/8.2)]² = [51.6*0.097]² = [5]² = 25

workelement 2 = [(2.58/0.05)*(0.6/9.2)]² = [51.6*0.065]² = [3.354]² = 11

workelememt 3 = [(2.58/0.05)*(0.5/4.4)]² = [51.6*0.113]² = [5.8308]² = 34

From the above analysis the sample size needed is "34".