This question is incomplete, the complete question is;
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 data lists the number of wins for track runners in the different starting positions. Calculate the chi-square test statistic to test the claim that the number of wins is uniformly distributed (equally likely) across the different starting positions. The results are based on 240 races.
starting position: 1 2 3 4 5 6
Number of wins : 44 33 50 32 45 36
options
a) 15.541
b) 9.326
c) 6.750
d) 12.592
Answer:
the chi-square test statistic is 6.75
Option c) 6.750 is the correct answer
Explanation:
Given that;
starting position: 1 2 3 4 5 6
Number of wins : 44 33 50 32 45 36
Given that we have 240 races
Using x² test.
we have to calculate the expected frequency
so
E(1) = 240 × 1/6 = 40
E(2) = 240 × 1/6 = 40
E(3) = 240 × 1/6 = 40
E(4) = 240 × 1/6 = 40
E(5) = 240 × 1/6 = 40
E(6) = 240 × 1/6 = 40
Now we know that,
x²_cal = [∑( Oi - Fi)²] / Fi
so
x²_cal = (44-40)²/40 + (33-40)²/40 + (50-40)²/40 + (32-40)²/40 + (45-40)²/40 + (35-40)²/40
= 0.4 + 1.225 + 2.5 + 1.6 + 0.625 + 0.4
= 6.75
Therefore the chi-square test statistic is 6.75
Option c) 6.750 is the correct answer