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QUESTION

A car company is attempting to develop a reasonably priced gasoline that will deliver improved gasoline mileages.

A car company is attempting to develop a reasonably priced gasoline that willdeliver improved gasoline mileages. As part of its development process, the companywould like to compare the effects of three types of gasoline (A, B and C) on gasolinemileage. For testing purposes, the company will compare the effects of gasoline types A,B and C on the gasoline mileage obtained by a popular mid-size car. 10 cars are randomlyselected to be assigned to each gasoline type (A, B and C), i.e., nA = nB = nC = 10. Andthe gasoline mileage for each test drive is measured.It is found that the sample means of the three groups are 34:92; 36:56 and 33:98. Andthe ANOVA table for the three-group model is summarized as following.ANOVA table for the three-mean modelSum of Squares D.F. Mean Squares F-stat p-valueBetween Group 17.0493 - - - 0.0013Within Group - - -Total 35.0773 -Let A; B and C be the mean mileages of gasoline types A, B and C respectively.Throughout, we assume the gasoline mileages all have normal distributions with a commonstandard deviation 2.(i) Please fill out the blanks in the table.(ii) Carry out an overall test to determine if there is significant evidence of a differenceamong A; B and C, at the significance level 1%.(iii) Construct a 95% confidence interval for B ô€€€A. You may replace a t-quantile witha standard normal quantile.