Question

A marketing specialist wants to estimate the average amount spent by visitors to an online retailers newly-designed website. From the data in a preliminary study she guesses that the standard deviation of the amount spent is about 14 dollars.

Question 1. How large a sample should she take to estimate the mean amount spent to within 5 dollars with 90% confidence? (Round your answer up to the next largest integer).

Answer 1

Solution :

Given that,

Population standard deviation = = 14

Margin of error = E = 5

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z_{0.05 = 1.645}

Z/2 = 1.645  

Z_/2 = 1.645

sample size = n = [Z_/2* / E] ²

n = [1.645 * 14 /5 ]²

n = 21

Sample size = n = 21