Suppose You Have Used a Randomized Block Design to Compare $\alpha = 0.025$

question 18

Essay

Suppose you have used a randomized block design to compare the effects of four different energy drinks on running speeds. Eight athletes were randomly selected. Each Monday each athlete was assigned an energy drink and their time to run four miles was recorded.
The results (in seconds) are shown below. Is there evidence of a difference in the probability distributions of the running times among the four different drinks? Apply the Friedman Fr-test to the data. Be sure to specify the null and alternative hypotheses. Use $\alpha = 0.025$

$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Drink }$
$\begin{array} { c c c c c } \hline \text { Runner } & 1 & 2 & 3 & 4 \\\hline 1 & 1275 & 1276 & 1323 & 1294 \\2 & 1179 & 1085 & 1201 & 1209 \\3 & 1279 & 1407 & 1341 & 1353 \\4 & 1306 & 1267 & 1322 & 1317 \\5 & 1209 & 1171 & 1265 & 1270 \\6 & 1368 & 1345 & 1398 & 1394 \\7 & 1270 & 1311 & 1307 & 1293 \\8 & 1293 & 1184 & 1321 & 1298 \\\hline\end{array}$

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Definitions:

PERT Analysis

Stands for Program Evaluation and Review Technique, a method used in project management to analyze the tasks involved in completing a project, especially the time needed to complete each task.

Beta Distribution

A statistical distribution ranging from 0 to 1, often used in Bayesian analysis and project forecasting, representing a family of probabilities.

Project Management

The discipline of initiating, planning, executing, controlling, and closing the work of a team to achieve specific goals and meet specific success criteria within a specified time.

Activity Times

Duration estimates for how long individual tasks within a project or process will take to complete.