Question

consider a sample of 53 football games, where 28 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
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<0.5 )
d. ( h_0:p = 0.5 )
( h_1:p
eq0.5 )

Explanation:

• The null hypothesis \(H_0\) is a statement of equality. In hypothesis testing for a proportion, when the claim is about a proportion \(p\), the null hypothesis typically assumes \(p\) is equal to a certain value. Here, the claim is related to comparing the proportion of home - team wins to \(0.5\), so \(H_0:p = 0.5\).
• 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", which translates to \(H_1:p>0.5\) in symbolic form.

Answer:

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