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 $\mu _ { 1 } = \mu _ { 2 } , \mu _ { 2 } = \mu _ { 3 } , \text { and } \mu _ { 1 } = \mu _ { 3 }$ ?
A) Actually, we do want to use three separate hypothesis tests.
B) The risk of type II error increases and becomes too high.
C) A hypothesis test for comparing two means does not exist.
D) The risk of type I error increases and becomes too high.

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 $\mu _ { 1 } = \mu _ { 2 } , \mu _ { 2 } = \mu _ { 3 } , \text { and } \mu _ { 1 } = \mu _ { 3 }$ ?
A) Actually, we do want to use three separate hypothesis tests.
B) The risk of type II error increases and becomes too high.
C) A hypothesis test for comparing two means does not exist.
D) The risk of type I error increases and becomes too high.

Quizplus · Accepted Answer

If we perform three separate hypothesis tests, each with a significance level of $\alpha = 0.05$, the overall risk of making at least one type I error (rejecting a true null hypothesis) increases. As a general rule, the more hypothesis tests we perform, the higher our risk of making at least one type I error. By using a single ANOVA test to compare all three means, we can control the overall risk of type I error at our desired significance level.

The Data Below Represent the Weight Losses for People on Three