Use the Wilcoxon Signed -Ranks Test to Test the Claim

question 149

Essay

Use the Wilcoxon signed -ranks test to test the claim that the matched pairs have differences_
that come from a population with a median equal to zero. Eleven runners are timed at 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 table. Use Wilcoxon's signed-ranks test and a significance
level of 0.05 to test the claim that the training has no effect on the times. $$\begin{array} { l l l l l l l l l l l l } \text { Before } & 12.1 & 12.4 & 11.7 & 11.5 & 11.0 & 11.8 & 12.3 & 10.8 & 12.6 & 12.7 & 10.7 \\\hline \text { After } & 11.9 & 12.4 & 11.8 & 11.4 & 11.2 & 11.5 & 12.0 & 10.9 & 12.0 & 12.2 & 11.1\end{array}$$

---

Definitions:

Progressive Tax

A taxation system where the tax rate increases as the taxable income or amount increases, placing a higher burden on those who have the ability to pay more.

Income Tax

A tax that governments impose on income generated by businesses and individuals within their jurisdiction, based on the income or profit earned.

Child Tax Credit

A tax benefit offered to taxpayers for each qualifying dependent child, aimed at reducing their tax liability.

Capitalist Economic System

An economic system where the means of production and distribution are privately or corporately owned and the operation is fueled by profit motive.