Question

If the inspection division of a county weights and measures department wants to estimate the mean amount of​ soft-drink fill in​ 2-liter bottles to within

± 0.01 liter with 95​% confidence and also assumes that the standard deviation is 0.07 ​liters, what sample size is​ needed?

n = _______

​(Round up to the nearest​ integer.)  

Answer 1

Solution :

Given that,

Population standard deviation = = 0.07

Margin of error = E = 0.01

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [1.96 *0.07 / 0.01]²

n = 188.23

Sample size = n = 189