Question

consider a sample of 49 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 )
identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is
(round to two decimal places as needed.)

Explanation:

Step1: Calculate sample proportion

Sample proportion $\hat{p}=\frac{x}{n}$, where $x = 27$ (number of home - team wins) and $n=49$ (sample size). So, $\hat{p}=\frac{27}{49}\approx0.551$.

Step2: Calculate test statistic

The formula for the test statistic $z$ in a one - sample proportion test is $z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}$, where $p_0 = 0.5$ (null hypothesis proportion).
Substitute the values:

$$
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$$

Answer:

The test statistic for this hypothesis test is $0.71$.