Question

A sports fan is studying the home court advantage in basketball playoff games. He finds that the home team won 55 out of 91 games studied. Test the hypothesis that the home team wins more than half of playoff games using α = 0.05.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p =0.5

H_a : p > 0.5

= x / n = 55 / 91 = 0.6044

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.6044 - 0.5/ [(0.5 * 0.5) / 91]

= 1.99

P-value = 0.0232

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that   the home team wins more than half of playoff games .