Question

Consider a population with population standard deviation σ=17. What is the minimum sample size required so that the margin of error of the 95% confidence interval of μ is not larger than 4?

70

18

69

71

Answer 1

Solution

standard deviation =   =17

Margin of error = E = 4

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z/2* / E] 2

n = ( 1.96* 17 / 4 )2

n =69.38

Sample size = n =70