Question

A sample is to be taken to develop an approximate 95% confidence interval estimate of the population mean. The population consists of 550 elements, and a pilot study resulted in

s = 80.

What is the minimum sample size needed if we want to develop an approximate 95% confidence interval with a width of 26? (Round your answer up to the nearest whole number.)

n =  

Answer 1

Solution

standard deviation =s =   =80

Margin of error = E = width / 2=26/2=13

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*80 /13 )2

n =145.48

Sample size = n =145 rounded