Reference no: EM13113280

A car company is attempting to develop a reasonably priced gasoline that will deliver improved gasoline mileages. As part of its development process, the company would like to compare the effects of three types of gasoline (A, B and C) on gasoline mileage. 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 randomly selected to be assigned to each gasoline type (A, B and C), i.e., nA = nB = nC = 10. And the 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. And the ANOVA table for the three-group model is summarized as following.

ANOVA table for the three-mean model
Sum of Squares D.F. Mean Squares F-stat p-value
Between Group 17.0493 - - - 0.0013
Within 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 common standard 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 difference among 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 with a standard normal quantile.