Question

Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test and if the variance of MPG is the same, Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 27 27 Refer to Exhibit 6. The test statistic and the p-value at 99% confidence level are

Answer 1

The given data is

Manufacturer A	Manufacturer B
32	28
27	22
26	27
26	24
25	24
29	25
31	28
27	27

Similar calculation for manufacturer B gave

So the test statistics is

and t follows t distribution with (8 + 8 -2) = 14

So subtituting values we get

so

so

P values = 2*P(T <= 1.9) where T follows t distribution with df = 14

So Computing from t tables/calculator =  2*P(T <= 1.9) = 0.08

Therefore at 0.01 level it is not significant. Hence null hypothesis is accepted at 99% level