Many Track Runners Believe That They Have a Better Chance

Short Answer

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. Find the rejection region used to test the claim that the probability of winning is the same regardless of starting position. Use α = 0.05. The results are based on 240 wins. $\begin{array}{c|cccccc}\text { Starting Position } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Number of Wins } & 45 & 36 & 33 & 44 & 50 & 32\end{array}$

A) $\chi ^ { 2 } > 11.070$
В) $x ^ { 2 } > 9.236$
C) $\chi ^ { 2 } > 15.086$
D) $\chi ^ { 2 } > 12.833$