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:

Interest Rate

The percentage of a sum of money charged for its use, typically expressed as an annual percentage.

Quadratic Form

An expression in algebra where the highest power of a variable is squared, typically in the format ax^2 + bx + c.

Completing The Square

A method used in algebra to solve quadratic equations by converting the equation to a perfect square trinomial.

Completing The Square

A method to solve quadratic equations by converting the quadratic equation into a perfect square trinomial, making it easier to solve.