Question

Problem 7-11 How many observations should a time study analyst plan for in an operation that has a standard deviation of 1.4 minutes per piece if the goal is to estimate the mean time per piece to within .3 minute with a confidence of 95.5 percent? (Do not round intermediate calculations. Round up your final answer to the next whole number.) Number of observations

Answer 1

standard deviation of population = s = 1.4 mins

let number of observations be n

standard deviation of sample = s/sqrt(n)

z value for confidence of 95.5% = 1.695

Upper limit = mean + z*s/sqrt(n)

Lower limit = mean - z*s/sqrt(n)

Confidence Interval = upper limit - lower limit = 2zs/sqrt(n) = 0.3

=> 2zs/sqrt(n) = 0.3

=> 2*1.695*1.4/sqrt(n) = 0.3

=> n = (2*1.695*1.4/0.3)^2 = 250.27

Hence, a sample of 251 observations is required