Question

During the first 15 weeks of the 2016 seasons, the home team won 137 of the 238 regular-season National Football League games. Is this strong evidence of a home field advantage in professional football? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p 0.5

n = 238

x = 137

= x / n = 137 / 238 = 0.5756

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.5756 - 0.5/ [(0.5 * 0.5) / 238]

= 2.334

Test statistic = 2.334

P(z > 2.334) = 0.0098

P-value = 2 * 0.0098 = 0.0196

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to support a home field advantage in professional football