Question

A research company for large retailers wants to know what percentage of shoppers use credit cards. How many randomly selected shoppers must they survey in order to estimate the proportion of shoppers who use credit cards to within 3.5% with 95% confidence?

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5.

margin of error = E = % = 0.035

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.035)2 * 0.5 * 0.5

= 784

Sample size =784