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

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