Many Track Runners Believe That They Have a Better Chance $\chi ^ { 2 }$

Multiple Choice

Many track runners 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 table displays the starting positions for the winners of 240 competitions. Calculate the chi-square test statistic $\chi ^ { 2 }$ used to test the claim that the probability of winning is the same regardless of starting position..
$\begin{array}{l|cccccc}\text { Starting Position } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Number of Wins } & 45 & 50 & 36 & 33 & 32 & 44\end{array}$

A) $9.326$
B) $12.592$
C) $6.750$
D) $15.541$