Question

If you want to be 95​% confident of estimating the population mean to within a sampling error of plus or minus ± 35 and the standard deviation is assumed to be 175​, what sample size is​ required?

Answer 1

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Solution

standard deviation =s =   =175

Margin of error = E = 35

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* 175/ 35 )2

n =96

Sample size = n =96