Question

If you want to be 95​% confident of estimating the population mean to within a sampling error of plus or minus 6 and the standard deviation is assumed to be 20​, what sample size is​ required?

The sample size required is __

​(Round up to the nearest​ integer.)  

Answer 1

Solution

standard deviation = =20

Margin of error = E =+/- 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 ( 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*20 /6 )2

n =42.68

Sample size = n =43