A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. For each pair of means, indicate which mean is larger or indicate that there is no significant difference. $$\begin{array} { l } \left( \mu _ { 1 } - \mu _ { 2 } \right) : ( 8,20 ) \ \left( \mu _ { 1 } - \mu _ { 3 } \right) : ( - 7,3 ) \ \left( \mu _ { 1 } - \mu _ { 4 } \right) : ( 9,21 ) \ \left( \mu _ { 2 } - \mu _ { 3 } \right) : ( - 21 , - 11 ) \ \left( \mu _ { 2 } - \mu _ { 4 } \right) : ( - 5,7 ) \ \left( \mu _ { 3 } - \mu _ { 4 } \right) : ( 12,22 ) \end{array}$$ A) $\mu _ { 1 } \mu _ { 2 }$; no significant difference between $\mu _ { 1 }$ and $\mu _ { 3 } ; \mu _ { 1 } \mu _ { 4 } ; \mu _ { 2 } \mu _ { 4 }$ B) no significant difference between $\mu _ { 1 }$ and $\mu _ { 2 }$; no significant difference between $\mu _ { 1 }$ and $\mu _ { 3 }$; $\mu _ { 1 } \mu _ { 4 } ; \mu _ { 2 } \mu _ { 4 }$ C) $\mu _ { 1 }

Question

A multiple-comparison procedure for comparing four treatment means produced the confidence intervals shown below. For each pair of means, indicate which mean is larger or indicate that there is no significant difference. $$\begin{array} { l } \left( \mu _ { 1 } - \mu _ { 2 } \right) : ( 8,20 ) \ \left( \mu _ { 1 } - \mu _ { 3 } \right) : ( - 7,3 ) \ \left( \mu _ { 1 } - \mu _ { 4 } \right) : ( 9,21 ) \ \left( \mu _ { 2 } - \mu _ { 3 } \right) : ( - 21 , - 11 ) \ \left( \mu _ { 2 } - \mu _ { 4 } \right) : ( - 5,7 ) \ \left( \mu _ { 3 } - \mu _ { 4 } \right) : ( 12,22 ) \end{array}$$ A) $\mu _ { 1 } > \mu _ { 2 }$; no significant difference between $\mu _ { 1 }$ and $\mu _ { 3 } ; \mu _ { 1 } > \mu _ { 4 } ; \mu _ { 2 } < \mu _ { 3 }$; no significant difference between $\mu _ { 2 }$ and $\mu _ { 4 } ; \mu _ { 3 } > \mu _ { 4 }$ B) no significant difference between $\mu _ { 1 }$ and $\mu _ { 2 }$; no significant difference between $\mu _ { 1 }$ and $\mu _ { 3 }$; $\mu _ { 1 } > \mu _ { 4 } ; \mu _ { 2 } < \mu _ { 3 } ;$ no significant difference between $\mu _ { 2 }$ and $\mu _ { 4 } ; \mu _ { 3 } > \mu _ { 4 }$ C) $\mu _ { 1 } < \mu _ { 2 }$; no significant difference between $\mu _ { 1 }$ and $\mu _ { 3 } ; \mu _ { 1 } < \mu _ { 4 } ; \mu _ { 2 } > \mu _ { 3 }$; no significant difference between $\mu _ { 2 }$ and $\mu _ { 4 } ; \mu _ { 3 } < \mu _ { 4 }$ D) $\mu _ { 1 } > \mu _ { 2 } ; \mu _ { 1 } < \mu _ { 3 } ; \mu _ { 1 } > \mu _ { 4 } ; \mu _ { 2 } < \mu _ { 3 } ; \mu _ { 2 } < \mu _ { 4 } ; \mu _ { 3 } > \mu _ { 4 }$

Quizplus · Accepted Answer

The confidence intervals indicate that $\mu_1 > \mu_2$ and $\mu_1 > \mu_4$ because their intervals are entirely positive. There is no significant difference between $\mu_1$ and $\mu_3$ or between $\mu_2$ and $\mu_4$ because their intervals include zero. $\mu_2 < \mu_3$ and $\mu_3 > \mu_4$ because their intervals are entirely negative and positive, respectively.

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