ANOVA Table Post Hoc Analysis
Tukey Simultaneous Comparison T-Values $($

ANOVA table
$\begin{array}{lrrrr}\hline\text { Source } & S S & d f & M S & F &p \text {-value }\\\hline \text { Treatment } & 6.000 & 3 & 1.9998 & 18.85&3.4E-05\\\hline\text { Error } & 1.486 & 14 & 0.1061 & \\\hline\text { Total } & 7.485 & 17 & &\end{array}$
Post hoc analysis
Tukey simultaneous comparison t-values $($ d.f. $=14)$
$\begin{array}{ccccc}&\text { Brand 3 }   \text { Brand 2 }  \text { Brand 4 }  \text { Brand 1 } \\&\quad1.40 \quad 2.28 \quad 2.58 \quad 2.95\\\begin{array}{ll}\text { Brand 3 } & 1.40 \\\text { Brand 2 } & 2.28 \\\text { Brand 4 } & 2.58 \\\text { Brand 1 } & 2.95\end{array}&\begin{array}{|l|l|l|l|}\hline & & & \\\hline 4.27 & & & \\\hline 5.38 & 1.35 & & \\\hline 7.09 & 3.07 & 1.63 &\quad\quad \\\hline\end{array}\end{array}$
The Excel/Mega-Stat output given above summarizes the results of a one-way analysis of variance in an attempt to compare the performance characteristics of four brands of vacuum cleaners. The response variable is the amount of time it takes to clean a specific size room with a specific amount of dirt.

-At a significance level of 0.05,the null hypothesis for the ANOVA F test is rejected.Analysis of the Tukey's simultaneous confidence intervals shows that at the significance level (experimentwise) of 0.05 we would conclude that,in regards to average time,

A) all four brands of vacuum cleaners differ from each other in terms of their performance.
B) brand 1 differs from brand 2,and brand 2 differs from brand 3 while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
C) brand 1 differs from brand 2,and brand 3 differs from brands 1,2 and 4,while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
D) only brand 3 differs from the other three brands (brands 1,2 and 3) ,while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
E) none of the four brands of vacuum cleaners differ from each other in terms of their performance.