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 6 dollars with 98% confidence? (Round your answer up to the next largest integer).

Answer 1

Solution :

Given that,

standard deviation =   =12

Margin of error = E = 6

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

sample size = n = [Z/2* / E] 2

n = ( 2.326*12 /6 )2

n =21.6

Sample size = n =22