A large tire company held an endofseason clearance sale List

A large tire company held an end-of-season clearance sale. Listed are sale prices for random samples of differenr models for three different brands. Is there sufficient eveidence at a=0.05 to conclude a difference in mean prices for the three brands? Using traditional hypothesis testing. Brand A: 112, 100, 120, 93, 119, 108, 103. Brand B: 125, 150, 103, 120, 131, 166, 158. Brand C: 113, 119, 136, 151, 162, 141, 150.

Solution

The test hypothesis:

Ho: there is no difference in mean prices for the three brands (i.e. null hypothesis)

Ha: there is a difference in mean prices for the three brands (i.e. alternative hypothesis)

The test statistic is

F=6.69

Given a=0.05, the critical value is F(0.95, df1=2, df2=18) =3.55 (from F table)

The rejection region is if F>3.55, we reject the null hypothesis.

Since F=6.69 is larger than 3.55, we reejct the null hypothesis.

So we can conclude that there is a difference in mean prices for the three brands