The data below represent the weight losses for people on three different exercise programs. $\begin{array}{ccc}
\text { Exercise A } & \text { Exercise B } & \text { Exercise } \mathbf{C} \
\hline 2.5 & 5.8 & 4.3 \
8.8 & 4.9 & 6.2 \
7.3 & 1.1 & 5.8 \
9.8 & 7.8 & 8.1 \
5.1 & 1.2 & 7.9
\end{array}$

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

Question

The data below represent the weight losses for people on three different exercise programs. $\begin{array}{ccc}
\text { Exercise A } & \text { Exercise B } & \text { Exercise } \mathbf{C} \
\hline 2.5 & 5.8 & 4.3 \
8.8 & 4.9 & 6.2 \
7.3 & 1.1 & 5.8 \
9.8 & 7.8 & 8.1 \
5.1 & 1.2 & 7.9
\end{array}$

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

Quizplus · Accepted Answer

Using three separate hypothesis tests increases the risk of a Type I error, which is the probability of incorrectly rejecting a true null hypothesis. This is known as the problem of multiple comparisons.

The Data Below Represent the Weight Losses for People on Three