An analyst from an energy research institute in California wishes to precisely e

Question

An analyst from an energy research institute in California wishes to precisely estimate a 99% 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 $0.06. What is the minimum number of gas stations that she should include in her sample if she uses the standard deviation estimate of $0.32, as reported in the popular press? Use Table 1. (Round intermediate calculations to 4 decimal places and "z" value to 2 decimal places. Round up your answer to the nearest whole number.)

An analyst from an energy research institute in California wishes to precisely estimate a 99% 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 $0.06. What is the minimum number of gas stations that she should include in her sample if she uses the standard deviation estimate of $0.32, as reported in the popular press? Use Table 1. (Round intermediate calculations to 4 decimal places and "z" value to 2 decimal places. Round up your answer to the nearest whole number.)

Explanation / Answer

Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.01% LOS is = 2.58 ( From Standard Normal Table )
Standard Deviation ( S.D) = 0.32
ME =0.06
n = ( 2.58*0.32/0.06) ^2
= (0.826/0.06 ) ^2
= 189.338 ~ 190      

Minimum number of gas stations are 190

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