Assume That the Data Below Come from Populations That Are $\mu _ { 1 }$

Essay

Assume that the data below come from populations that are normally distributed with the same variance. Let $\mu _ { 1 }$ be the mean for treatment $1 , \mu _ { 2 }$ the mean for treatment 2 , and $\mu _ { 3 }$ the mean for treatment 3 . In a test of $\mathrm { H } _ { 0 }$ : $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ versus $\mathrm { H } _ { 1 }$ : at least one of the means is different, the null hypothesis is rejected at the $\alpha = 0.05$ level of significance. Use Tukey's test to determine which pairwise means differ using a familywise error rate of $\alpha = 0.05$ . Give the $\mathrm { P }$ -value for each of the pairwise tests and state your conclusion.
$\begin{array}{c|c|c|c}\text { Block } & \text { Treatment 1 } & \text { Treatment 2 } & \text { Treatment 2 } \\\hline 1 & 7.2 & 6.6 & 6.1 \\2 & 6.9 & 7.5 & 6.7 \\3 & 8.2 & 8.6 & 8.3 \\4 & 9.7 & 9.3 & 8.8 \\5 & 9.4 & 10.2 & 9.5 \\6 & 10.3 & 9.8 & 9.2\end{array}$