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

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 $\chi _ { 0 } ^ { 2 }$ 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.
$\begin{array}{l|cccccc}\text { Starting Position } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Number of Wins } & 32 & 45 & 50 & 36 & 33 & 44\end{array}$

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