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. $$\begin{array} { l }
\left( \mu _ { 1 } - \mu _ { 2 } \right) : ( 7,21 ) \
\left( \mu _ { 1 } - \mu _ { 3 } \right) : ( - 6,2 ) \
\left( \mu _ { 1 } - \mu _ { 4 } \right) : ( 10,20 ) \
\left( \mu _ { 2 } - \mu _ { 3 } \right) : ( - 19 , - 13 ) \
\left( \mu _ { 2 } - \mu _ { 4 } \right) : ( - 3,5 ) \
\left( \mu _ { 3 } - \mu _ { 4 } \right) : ( 10,24 )
\end{array}$$
A) $\overline { 41 } \overline { 23 }$
B) $24 \overline { 13 }$
C) $\overline { 42 } \overline { 13 }$
D) 4213

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. $$\begin{array} { l } 
\left( \mu _ { 1 } - \mu _ { 2 } \right) : ( 7,21 ) \
\left( \mu _ { 1 } - \mu _ { 3 } \right) : ( - 6,2 ) \
\left( \mu _ { 1 } - \mu _ { 4 } \right) : ( 10,20 ) \
\left( \mu _ { 2 } - \mu _ { 3 } \right) : ( - 19 , - 13 ) \
\left( \mu _ { 2 } - \mu _ { 4 } \right) : ( - 3,5 ) \
\left( \mu _ { 3 } - \mu _ { 4 } \right) : ( 10,24 )
\end{array}$$
A) $\overline { 41 } \overline { 23 }$
B) $24 \overline { 13 }$
C) $\overline { 42 } \overline { 13 }$
D) 4213

Quizplus · Accepted Answer

The confidence intervals that do not include zero indicate a significant difference between the means. For intervals that include zero, the means are not significantly different. From the given intervals:- $(\mu_1 - \mu_2): (7,21)$ indicates $\mu_1 > \mu_2$.- $(\mu_1 - \mu_3): (-6,2)$ includes zero, so $\mu_1$ and $\mu_3$ are not significantly different.- $(\mu_1 - \mu_4): (10,20)$ indicates $\mu_1 > \mu_4$.- $(\mu_2 - \mu_3): (-19, -13)$ indicates $\mu_3 > \mu_2$.- $(\mu_2 - \mu_4): (-3,5)$ includes zero, so $\mu_2$ and $\mu_4$ are not significantly different.- $(\mu_3 - \mu_4): (10,24)$ indicates $\mu_3 > \mu_4$.Thus, $\mu_3$ is not significantly different from $\mu_1$, but it is greater than both $\mu_2$ and $\mu_4$, and $\mu_2$ and $\mu_4$ are not significantly different from each other but are less than $\mu_1$. Therefore, the ranking from smallest to largest with groups that are not significantly different connected is $\overline { 42 } \overline { 13 }$.

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