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

question 23

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 $H _ { 0 }$ : $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ 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 P-value for each of the pairwise tests and state your conclusion.
$\begin{array}{c|c|c|c}\text { Block } & \text { Treatment 1 } & \text { Treatment 2 } & \text { Treatment 3 } \\\hline 1 & 17.3 & 19.1 & 16.9 \\2 & 17.9 & 21.4 & 17.5 \\3 & 17.2 & 23.3 & 18.6 \\4 & 19.1 & 21.6 & 20.1 \\5 & 20.8 & 23.7 & 19.6\end{array}$

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Definitions:

Crisis Experience

An emotionally significant event or radical change of status in a person's life, which can lead to a period of psychological upheaval.

Outcome of Crisis

The resolution or final consequences resulting from a period of significant challenge, change, or instability.

Initiative

The ability to assess and initiate things independently, often taking charge in situations or starting something new without being prompted.

Locus of Control

A psychological concept that refers to individuals' beliefs about the extent to which the outcomes of their actions are under their own control (internal locus) or beyond their control (external locus).