Preliminary Data Analyses Indicates That Use of a Paired Wilcoxon $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$

question 57

Essay

Preliminary data analyses indicates that use of a paired Wilcoxon signed-rank test is reasonable. Perform the hypothesistest by using a paired Wilcoxon signed-rank test. Assume that the null hypothesis is $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-Eleven runners are timed in the 100-meter dash and are timed again one month later after following a new training program. The times (in seconds)are shown in the following table. $$\begin{array} { l l l l l l l l l l l l } \text { Before } & 12.1 & 12.4 & 11.7 & 11.5 & 11.0 & 11.8 & 12.3 & 10.8 & 12.6 & 12.7 & 10.7 \\ \hline \text { After } & 11.9 & 12.4 & 11.8 & 11.4 & 11.2 & 11.5 & 12.0 & 10.9 & 12.0 & 12.2 & 11.1 \end{array}$$ At the 10% significance level, do the data provide sufficient evidence to conclude that the training is effective in reducing times in the 100-meter dash?

---

Definitions:

Priming Effects

The phenomenon whereby exposure to a stimulus influences a response to a subsequent stimulus, without conscious guidance or intention.

Perceptual Segregation

The process by which the sensory systems distinguish different stimuli into clearly defined categories, allowing for object recognition and differentiation.

Musical Instrument

A device created or adapted to make musical sounds.

Dichotic Listening

A psychological test in which different audio streams are presented to each ear, used to investigate selective attention within the auditory system.