Test the Claim That the Samples Come from Populations with the Same

Essay

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance.
-A consumer magazine wants to compare the lifetimes of ballpoint pens of three different types. The magazine takes a random sample of pens of each type in the following table.

$\begin{array} { l } \text { Brand A}&\text { Brand B}&\text { Brand C }\\\hline260&181&238\\218&240&257\\184&162&241\\219&218&213\end{array}$
Do the data indicate that there is a difference in mean lifetime for the three brands of ballpoint pens? $\text { Use } \alpha = 0.01 \text {. }$