The data below represent the weight losses for people on three different exercise programs. $$\begin{array} { c c c }
\text { Exercise A } & \text { Exercise B } & \text { Exercise C } \
\hline 2.5 & 5.8 & 4.3 \
8.8 & 4.9 & 6.2 \
7.3 & 1.1 & 5.8 \
9.8 & 7.8 & 8.1 \
5.1 & 1.2 & 7.9
\end{array}$$ 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 $\mu _ { 1 } = \mu _ { 2 } , \mu _ { 2 } = \mu _ { 3 } \text {, and } \mu _ { 1 } = \mu _ { 3 } \text { ? }$

Question

The data below represent the weight losses for people on three different exercise programs. $$\begin{array} { c c c } 
\text { Exercise A } & \text { Exercise B } & \text { Exercise C } \
\hline 2.5 & 5.8 & 4.3 \
8.8 & 4.9 & 6.2 \
7.3 & 1.1 & 5.8 \
9.8 & 7.8 & 8.1 \
5.1 & 1.2 & 7.9
\end{array}$$ 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 $\mu _ { 1 } = \mu _ { 2 } , \mu _ { 2 } = \mu _ { 3 } \text {, and } \mu _ { 1 } = \mu _ { 3 } \text { ? }$

Quizplus · Accepted Answer

The Answer is As we increase the number of individual tests of significance, we increase the risk of finding a difference
by chance alone. That is, the risk of a type I error is too high.

The Data Below Represent the Weight Losses for People on Three