Question

Consider a sample of 53 football​ games, where 32 of them were won by the home team. Use a 0.10 significance level to test the claim that the probability that the home team wins is greater than​ one-half.

Answer 1

H0: Null hypothesis: P 0.5

HA: Alternative hypothesis: P > 0.5

n = sample size = 53

p = sample proportion = 32/53 = 0.6038

P = Population proportion = 0.5

Q = 1 - P = 0.5

The test statistic is:
Z = (p - P)/SE

= (0.6038 - 0.5)/0.0687 = 1.5109

= 0.10

One tail - right side test

From Table, critical value of Z = 1.28

Since the calculated value of Z = 1.5109 is greaer than critical value of Z = 1.28, H0 is rejected.

Conclusion:

The data supports the claim that the probability that the home team wins is greater than one-half.