Many Track Hurdlers Believe That They Have a Better Chance $x _ { 0 } ^ { 2 }$

question 12

Multiple Choice

Many track hurdlers believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track hurdlers in the different starting positions. Find the critical value $x _ { 0 } ^ { 2 }$ to test the claim that the probabilities of winning are the same in the different positions. Use $\alpha$

=0.05 . The results are based on 240 wins.
$\begin{array} { l | c c c c c c } \text { Starting Position } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Number of Wins } & 45 & 36 & 32 & 33 & 44 & 50\end{array}$

• A) 11.070
• B) 9.236
• C) 15.086
• D) 12.833

---

Definitions:

Active Portfolio

In the context of the Treynor-Black model, the portfolio formed by mixing analyzed stocks of perceived nonzero alpha values. This portfolio is ultimately mixed with the passive market-index portfolio.

Nonsystematic Variance

The portion of an investment's variance that is attributable to the investment's specific factors, as opposed to the overall market movement.

Market Index

A market index is a hypothetical portfolio of investment holdings which represents a segment of the financial market.

R-squares

A statistical measure in finance that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.