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 plus or minus0.02 liter with 95?% confidence and also assumes that the standard deviation is 0.09 ?liters, what sample size is? needed?

Answer 1

Solution :

Given that,

standard deviation = = 0.09

margin of error = E = 0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Sample size = n = ((Z_/2 * ) / E)²

= ((1.960 * 0.09) / 0.02)²

= 77.79

Sample size = 78