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:

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The present value of a future amount of money or sequence of cash flows when discounted at a certain rate of return.

Annual Investment

The total sum of money invested in a particular option or portfolio in a year.

Present Values

The current value of a future amount of money or stream of cash flows given a specified rate of return.