Question

A marketing specialist wants to estimate the average amount spent by visitors to an online retailer's newly-designed website. From the data in a preliminary study she guesses that the standard deviation of the amount spent is about 12 dollars.

Question 1. How large a sample should she take to estimate the mean amount spent to within 5 dollars with 95% confidence? (Round your answer up to the next largest integer).

Answer 1

Solution :

Given that,

standard deviation = = 12

margin of error = E = 5

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 * 12) / 5)²

= 22.12 = 23

Sample size = 23