Question

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 to test the claim that the probabilities of winning are the same in the different positions. Use 0.05. The results are based on 240 wins.

Answer 1

χ² = 6.75

χ² Critical = 11.07

Explanation:

Given the data :

Expected winnings ;

1/n * total number of wins

Total number of wins = 240

n = number of starting positions = 6

Expected winnings = 1/6 * 240 = 40

Using χ² test :

χ² = Σ(O - E)² / E

O = Observed ; E = Expected

χ² = (32 - 40)^2 / 40 + (33 - 40)^2 / 40 + (45 - 40)^2 / 40 + (44 - 40)^2 / 40 + (50 - 40)^2 / 40 + (36 - 40)^2 / 40

= 6.75

χ² Critical at α = 0.05 ; df = n - 1 ; df = 5

χ² Critical = 11.07

Since χ² < χ² Critical ; WE fail to reject H0.