Question

2. An automobile factory wants to determine whether a particular model car manufactured by the com- pany gets the same mileage with high and low octane gasoline. A sample is selected among the cars of this model manufactured last month and randomly split into two groups of 16 cars each. One group of cars is driven in a course with low octane gas, and the other group of cars is driven in the same course with high octane gas. The results in miles per gallon are as follows: Sample 1 Low octane gasoline X= 30 s1 = 3 n = 16 Sample 2 High octane gasoline X2 = 33 82 = 10 n = 16 Run a test at significance level a = 0.1 to decide whether the model gets equal mileage with low and high octane gasoline assuming that the standard deviation of mileage is the same regardless of the octane grade of gas.

Answer 1

(2) Here we have M,516, 7, = 30, S1E3 33, S2 - YO 22:16 20.10 Degree of freedom 29.91 van vous voye 23 Hypo meses: Hoi 14, - M2-0 Hai M, - M2 70 Test statistic of test tě - az 16 = 30 - 33 p =/2.75 L Va + stoje pualue at t = 2.75 and df = 29 . pualne = T11841 2.75,29,2)-70.0182 7 = 10.0102] since pualue < 0.20 we regect Ho.. conclusion : There is sufficient evidence to resect the models get different claim and we can conclude that millege with law and high octane gasoline._