We are interested in estimating the mean price of unleaded gasoline in the area. The following will give us this estimation. Gas Prices of 45 gas stations are

$3.52 x 7, $3.53 x 4, $3.54 x 6, $3.55 x 25, $3.56 x 3.

a) Determine a 99% confidence interval for the mean gasoline prices.

b) Give an interpretation of this confidence interval.

c) Last year, April 2013, AAA gave an average gasoline price of $3.761 in Milwaukee. According to your data can we say there is a significant difference in the mean gasoline prices compared to AAA a year ago?

i. Give the null and alternative hypothesis

ii. Describe the assumptions of this hypothesis test. Determine if the test statistic you are using is appropriate. Fully explain.

iii. Determine the p-value

iv. Give a conclusion of this hypothesis test. Use α = 0.01.

v. Compare the results of the significance test to the 99% confidence interval for the mean gasoline price per gallon. Does the conclusion in part iv still hold for the confidence interval? Fully explain.