Question

To estimate with 95% confidence the mean of a normal population whose standard deviation is assumed to be 4 and the maximum allowable sampling error is assumed to be 1, what must the random sample size be? Make sure to round your answers up to the nearest whole number.

Answer 1

Solution :

Given that,

Population standard deviation = = 4

Margin of error = E = 1

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = Z_0.025 = 1.96  

sample size = n = [Z_/2* / E] ²

n = [1.96 * 4 / 1]²

n = 61.46

Sample size = n = 62