Question

We are estimating the population mean using a 95% confidence interval. How many subjects need to be sampled if we want the length of confidence interval to be at most 5? Assume that the population standard deviation is 20.

Answer 1

Solution

standard deviation =   =20

Margin of error = E = 5

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

n = ( 1.96* 20 / 5)2

n =61.4656

Sample size = n =61