Question

A store wants to determine the average amount that a shopper spends in its store with an error of +/-$5 at 95% confidence. If previous analysis has shown that the standard deviation of past sales amounts is $25, how many shoppers do they need to sample? How many shoppers need to be sampled if they want 99%confidence?

Answer 1

Solution :

Given that,

Population standard deviation = = 25

Margin of error = E = 5

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

sample size = n = (Z_/2* / E) ²

n = (2.576 * 25 / 5)²

n = 165.89

n = 166

Sample size = 166