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Many Track Hurdlers Believe That They Have a Better Chance χ02\chi _ { 0 } ^ { 2 }

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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 χ02\chi _ { 0 } ^ { 2 } to test the claim that the probabilities of winning are the same in the different positions. Use α=0.05\alpha = 0.05 . The results are based on 240 wins.
 Starting Position 123456 Number of Wins 324550363344\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}


Definitions:

Angular Movements

Movements of bones around a joint axis, including actions like bending, straightening, or rotating.

Circular Movements

Movements that occur around an axis, such as rotation, involving a body part moving in a circular path.

Abduction

The movement of a body part away from the midline of the body or the principal axis of a limb.

Adduction

Adduction is the movement of a body part towards the central axis of the body.

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