The Data Below Represent the Weight Losses for People on Three

Essay

The data below represent the weight losses for people on three diets. $\begin{array}{lcc}\text { Diet A } & \text { Diet B } & \text { Diet C } \\\hline 1.75 & 3.8 & 4.8 \\8.8 & 4.9 & 6.2 \\7.3 & 1.1 & 5.8 \\9.8 & 7.8 & 8.1 \\5.1 & 1.2 & 6.9\end{array}$
If we want to test the claim that the three size categories have the same means, why don't we use three separate hypothesis tests for $\mu _ { 1 } = \mu _ { 2 } , \mu _ { 2 } = \mu _ { 3 }$ , and $\mu _ { 1 } = \mu _ { 3 }$ ?