Question

Suppose you want to estimate a population mean correct to within 0.25 with probability equal to 0.95. You do not know the population variance but you are given that the observations will range in value between 20 and 40. Then the approximate sample size that will produce the desired accuracy of the estimate is __________.

Answer 1

Solution :

Given that,

Population standard deviation = = 40 - 20 / 4 = 5 ( range rule thumb)

Margin of error = E = 0.25

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = 1.95

sample size = n = [Z_/2* / E] ²

n = [1.95 *5 / 0.25]²

n = 1521

Sample size = n = 1521