Question

A gambler claims that horses in a horse race that start closer to the rail have an advantage over horses that start further from the rail because the horses closer to the rail have a shorter distance to travel to win the race. In a sample of 120 races, the following data show the number of winners from each starting position. If the starting position is not a factor then each starting position should have produced 20 winners.
Starting position: 1 2 3 4 5 6
# of Winners: 25 22 18 19 21 15
Test the hypothesis at the 5% level of significance to see if starting position is a factor.

Answer 1

Answer:

Hence, the p-value ( 0.699986) > 0.05,  FAIL TO REJECT THE NULL HYPOTHESIS

there is no significant evidence that starting position is a factor in horse races

Step-by-step explanation:

Given the data in the question;

Starting position:     1     2     3     4     5     6

# of Winners:         25   22   18   19    21   15

Mean x" (E) = (25+22+18+19+21+15)/6 = 120/6 = 20

Observed/Expected value table;

O       E            ((O-E)²) / E

25    20            1.25

22    20            0.2

18     20            0.2

19     20           0.05

21     20           0.05

15     20           1.25

∑                         3

so using chi square = ∑(((O-E)²) / E) = 3

DF = n-1 = 6-1 = 5

then, the critical chi square value is;

significance level = 0.05

chi square( critical ) = 11.07049769

from table;

p - value = 0.699986

Hence, the p-value ( 0.699986) > 0.05,  FAIL TO REJECT THE NULL HYPOTHESIS

there is no significant evidence that starting position is a factor in horse races