Consumer Reports wants to determine if the average lifetimes

Consumer Reports wants to determine if the average lifetimes of ballpoint pens of three different types are the same.The magazine takes a random sample of pens of each type.Results are shown in the following table.

Brand 1

Brand 2

Brand 3

260

181

238

218

240

257

184

162

241

219

218

213

At the 0.05 level of significance is Consumer Reports correct?

Solution

The test hypothesis:

Ho: all means are equal. (i.e. null hypothesis)

Ha: at least one mean is different (i.e. alternative hypothesis)

The test statistic is

F=1.62

The p-value of F test is 0.2507 (from F table)

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can conclude that Consumer Reports is correct