Question

consider a sample of 48 football games, where 27 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 one - half. identify the null and alternative hypotheses for this test. choose the correct answer below.

a. ( h_0: p = 0.5 ) ( h_1: p>0.5 )
b. ( h_0: p>0.5 ) ( h_1: p = 0.5 )
c. ( h_0: p = 0.5 ) ( h_1: p
eq0.5 )
d. ( h_0: p = 0.5 ) ( h_1: p<0.5 )

Explanation:

• The null hypothesis \(H_0\) is a statement of equality. Here, the claim is about the probability \(p\) (probability that home - team wins). The initial assumption (null hypothesis) for a proportion test when comparing to a specific value (in this case \(0.5\)) is \(H_0:p = 0.5\).
• The alternative hypothesis \(H_1\) is the claim we are testing. The claim is that “the probability that the home team wins is greater than one - half”, so \(H_1:p>0.5\).

Answer:

A. \(H_0:p = 0.5\), \(H_1:p>0.5\)