Question

If you want to be 95​% confident of estimating the population mean to within a sampling error of plus or minus ± 5 and the standard deviation is assumed to be 17​, what sample size is​ required? The sample size required is ________

Answer 1

:

Solution

standard deviation =s =   =17

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 ( 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*17 / 5 )2

n =44.408

Sample size = n =45