Question

A statistician employed by a consumer testing organization reported that at 95% confidence he has determined that his estimate content of a particular soft drink is within 0.3 ounces of the true population average content. He forgot to report the size of the sample selected. Assuming the population standard deviation is 1.18, determine the size of the sample.

Answer 1

Solution :

Given that,

standard deviation = = 1.18

margin of error = E = 0.3

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 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 1.18) / 0.3)²

= 59

Sample size = 59