Question

Some track and field athletes feel that they are more likely to win a race if they start on the inside lane. The data above shows the number of winners for each lane, from Lane 1, the innermost lane and closest to the infield, out to Lane 6, the outermost lane and furthest from the infield. The data lists how many wins were recorded in each lane over 240 races.

Find the value of x^{2} to show whether the chances of winning are equal in each lane.
A. 2.594
B. 2.6
C. 3.666
D. 6

Answer 1

2.6

Explanation:

The χ² = (observed - Expected)²/Expected

The expected wins :

n = 6

(45+33+44+39+42+37) / 6 = 40

χ² = (45-40)²/40 + (33-40)²/40 + (44-40)²/40 + (39-40)²/40 + (42-40)²/40 + (37-40)²/40

χ² = 0.625 + 1.225 + 0.4 + 0.025 + 0.1 + 0.225

χ² = 2.6