Question

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is 1.6? The population standard deviation is known to be 10.36.

a) n = 102

b) n = 103

c) n = 161

d) n = 162

Answer 1

Given that,

standard deviation = = 10.36

margin of error = E = 1.6

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

Sample size = n = [(Z/2 * ) / E]2

= ((1.96 *10.36) /1.6)2

= 161.06

Sample size = 162

Correct option = d) n = 162