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

question 30

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.
$\begin{array}{c|c|c|c}\text { Block } & \text { Treatment 1 } & \text { Treatment 2 } & \text { Treatment 2 } \\\hline 1 & 7.2 & 6.6 & 6.1 \\2 & 6.9 & 7.5 & 6.7 \\3 & 8.2 & 8.6 & 8.3 \\4 & 9.7 & 9.3 & 8.8 \\5 & 9.4 & 10.2 & 9.5 \\6 & 10.3 & 9.8 & 9.2\end{array}$

---

Definitions:

Plasticity

The capacity of the brain to change and adapt in response to experience, learning, or injury.

Resilience

The ability of an individual to recover from adversity, trauma, tragedy, threats, or significant stress and to adapt well over time.

Plasticity

The brain's capacity to change and adapt in response to experiences, learning, and injury.

Changing Resource Allocations

The process of adjusting how resources are distributed or assigned, often in response to shifts in needs, priorities, or availability.