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

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