Suppose a study reports that the average price for a gallon of self-serve regula

Question

Suppose a study reports that the average price for a gallon of self-serve regular unleaded gasoline is $3.16. You believe that the figure is higher in your area of the country. You decide to test this claim for your part of the United States by randomly calling gasoline stations. Your random survey of 25 stations produces the following prices (all in $). Assume gasoline prices for a region are normally distributed. Do the data you obtained provide enough evidence to reject the claim? Use a 1% level of significance.

3.27 3.29 3.16 3.20 3.37

3.20 3.23 3.19 3.20 3.24

3.16 3.07 3.27 3.09 3.35

3.15 3.23 3.14 3.05 3.35

3.21 3.14 3.14 3.07 3.10

Explanation / Answer

Sample mean = xbar = 3.19
Sample Std Dev = s = 0.0889

Ho: = 3.16
Ha: > 3.16

Test Statistic = t0 = (xbar - )/(s/sqrt(n))
t0 = (3.19 - 3.16)/(0.0889/5)
t0 = 1.687

t/n-1 = t0.01/25-1 = t0.01,24 = 2.492

For this one tailed test, we reject Ho if t0 > t/n-1. In this case 1.687 > 2.492 is false, so we fail to reject H0. The data doesn't provide enough evidence to test the claim.

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