#28 An analyst from an energy research institute in California wishes to precise
ID: 3160374 • Letter: #
Question
#28
An analyst from an energy research institute in California wishes to precisely estimate an 95% 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 $0.09. 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.)
Do you feel confident that the manager’s discount strategy has worked?
#28
An analyst from an energy research institute in California wishes to precisely estimate an 95% 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 $0.09. 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
a.
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 0.32
ME =0.09
n = ( 1.96*0.32/0.09) ^2
= (0.627/0.09 ) ^2
= 48.565 ~ 49
b.No, there is only a small chance (less than 5%) of getting 51 or more customers without the discount.
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