Following are the free throw statistics from basketball great Larry Bird’s two seasons.
Total pairs of throws: 338
Pairs where both throws missed: 5
Pairs where one missed: 82
Pairs where both made: 251
Test the hypothesis that Mr Bird’s free throw follows binomial distribution with p = 0.8.
H0 = Bird’s free throw probability of success followed a binomial distribution with p = 0.8
HA = The distribution did not follow a binomial distribution with p = 0.8
We will use chi-square Goodness of Fit to test the hypothesis. The probabilities of making 0, 1 and 2 free throws for a person with a probability of success of 0.8 is
bino_prob <- dbinom(0:2, 2, 0.8) 0.04 0.32 0.64The chi-square test is:
chisq.test(child_perHouse, p = bino_prob, rescale.p = TRUE)
Chi-squared test for given probabilities
data: child_perHouse
X-squared = 17.256, df = 2, p-value = 0.000179
