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 3 dollars with 90% confidence? (Round your answer up to the next largest integer).

Answer 1

Solution :

Given that,

standard deviation = =12

Margin of error = E = 3

so,

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )  

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

n = ( 1.645 * 12 / 3)2

n =43.2964

Sample size = n =44 (rounded)