Question

Suppose the population standard deviation, σ, is 30 based upon previous studies. We would like to estimate the population mean within ±10 of its true value, at a significance level of .05 (95% Confidence interval). What sample size should be taken?

Answer 1

Solution :

Given that,

standard deviation = = 30

margin of error = E = 10

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Sample size = n = ((Z_/2 * ) / E)²

= ((1.960 * 30) / 10)²

= 34.57

= 35

Sample size = 35