Question

consider a sample of 50 football games, where 31 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 the sample proportion

The sample proportion $\hat{p}$ is calculated as $\hat{p}=\frac{x}{n}$, where $x = 31$ (number of home - team wins) and $n=50$ (sample size). So, $\hat{p}=\frac{31}{50}=0.62$.

Step2: Calculate the test statistic

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

$$
LATEXBLOCK0
$$

Answer:

The test statistic for this hypothesis test is $1.70$ (rounded to two decimal places).