A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. Rank the means from smallest to largest. Use solid lines to connect those
Means which are not significantly different. $$\begin{array} { l }
\left( \mu _ { A } - \mu _ { B } \right) : ( 16,36 ) \
\left( \mu _ { A } - \mu _ { C } \right) : ( 7,23 ) \
\left( \mu _ { A } - \mu _ { D } \right) : ( 4,20 ) \
\left( \mu _ { B } - \mu _ { C } \right) : ( - 18 , - 4 ) \
\left( \mu _ { B } - \mu _ { D } \right) : ( - 20 , - 8 ) \
\left( \mu _ { C } - \mu _ { D } \right) : ( - 9 , - 2 )
\end{array}$$
A) B $\overline { C D } A$
B) $\mathrm { B } C \overline { \mathrm { AD } }$
C) $B C D A$
D) $\overline { C D } B A$

Question

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. Rank the means from smallest to largest. Use solid lines to connect those
Means which are not significantly different. $$\begin{array} { l } 
\left( \mu _ { A } - \mu _ { B } \right) : ( 16,36 ) \
\left( \mu _ { A } - \mu _ { C } \right) : ( 7,23 ) \
\left( \mu _ { A } - \mu _ { D } \right) : ( 4,20 ) \
\left( \mu _ { B } - \mu _ { C } \right) : ( - 18 , - 4 ) \
\left( \mu _ { B } - \mu _ { D } \right) : ( - 20 , - 8 ) \
\left( \mu _ { C } - \mu _ { D } \right) : ( - 9 , - 2 )
\end{array}$$
A) B $\overline { C D } A$
B) $\mathrm { B } C \overline { \mathrm { AD } }$
C) $B C D A$
D) $\overline { C D } B A$

Quizplus · Accepted Answer

The confidence intervals for the differences between means indicate which means are significantly different from each other. For example, the interval for $(\mu_A - \mu_B)$ being entirely positive (16, 36) means $\mu_A > \mu_B$. Similarly, all other intervals being positive or negative without crossing zero indicates a clear difference between the means they compare. The intervals for $(\mu_B - \mu_C)$, $(\mu_B - \mu_D)$, and $(\mu_C - \mu_D)$ being entirely negative indicate $\mu_B > \mu_C > \mu_D$. However, since the intervals comparing $\mu_A$ with $\mu_B$, $\mu_C$, and $\mu_D$ are all positive and do not overlap with the intervals comparing $\mu_B$, $\mu_C$, and $\mu_D$ among themselves, it indicates $\mu_A$ is the largest mean. Therefore, the ranking from smallest to largest is $B \overline{CD} A$, where $C$ and $D$ are not significantly different from each other.

A Multiple-Comparison Procedure for Comparing Four Treatment Means Produced the Confidence