Homework SourseAn analyst from an energy research institute in California w
An analyst from an energy research institute in California wishes to precisely estimate a 93% 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 $0.07. What is the minimum number of gas stations that she should include in her sample if she uses the standard deviation estimate of $0.22, as reported in the popular press? Use Table 1. (Do not round intermediate calculations. Round \"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 93% 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 $0.07. What is the minimum number of gas stations that she should include in her sample if she uses the standard deviation estimate of $0.22, as reported in the popular press? Use Table 1. (Do not round intermediate calculations. Round \"z\" value to 2 decimal places. Round up your answer to the nearest whole number.) |
Solution
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.07% LOS is = 1.81 ( From Standard Normal Table )
Standard Deviation ( S.D) = 0.22
ME =0.07
n = ( 1.81*0.22/0.07) ^2
= (0.398/0.07 ) ^2
= 32.36 ~ 33
