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 2 dollars with 99% confidence? (Round your answer up to the next largest integer).

Answer 1

Solution :

Given that,

standard deviation = = 12

margin of error = E = 2

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

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

= ((2.576 * 12) / 2 )2

= 239

Sample size = 239