Question

Consider a sample of 45 football games where 33 of them were won by the home team. use a 0.01 significance level to test the claim that the probability that the home team wins is greater than 1/2.

Answer 1

To Test :-

H0 :- P = 0.5

H1 :- P > 0.5

n = 45
P = X / n = 0.7333

Test Statistic :-


Z = 3.13

Test Criteria :-
Reject null hypothesis if

= 3.13 > 2.326, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z > 3.13 )
P value = 0.0009
Reject null hypothesis if P value <
Since P value = 0.0009 < 0.01, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that the probability that the home team wins is greater than 1/2 at 1% level of significance.