An analyst from an energy research institute in California w

An analyst from an energy research institute in California wishes to precisely estimate a 90% confidence interval for the average price of unleaded gasoline in the state. In particular, she does not want the sample mean to deviate from the population mean by more than $0.08. What is the minimum number of gas stations that she should include in her sample if she uses the standard deviation estimate of $0.35, as reported in the popular press?

Solution

Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.1% LOS is = 1.64 ( From Standard Normal Table )
Standard Deviation ( S.D) = 0.35
ME =0.08
n = ( 1.64*0.35/0.08) ^2
= (0.574/0.08 ) ^2
= 51.481 ~ 52