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).
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)
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