Question

You need to estimate the mean number of travel days per year for outside salespeople. The mean of a small pilot study was 150 days, with a standard deviation of 36 days. 

If you must estimate the population mean within 10 days, how many outside salespeople should you sample? Use the 95% confidence level. 

Number of outside salespeople _______ 

Z Distribution Table:

Answer 1

Given that,

standard deviation =  $\sigma$ =36

Margin of error = E = 10

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z_$\alpha$/2 = Z _0.025 = 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_$\alpha$/2* $\sigma$ / E] ²

n = ( 1.96* 36 / 10 )²

^{n=49.787 ( rounded)}

n =50

Sample size = n =50