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 )

identify the test statistic for this hypothesis test.

the test statistic for this hypothesis test is (square)
(round to two decimal places as needed)

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}=\frac{x}{n}$, where $x = 28$ (number of home - team wins) and $n=53$ (sample size). So, $\hat{p}=\frac{28}{53}\approx0.5283$.

Step2: Calculate the 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 $p_0 = 0.5$ (the proportion in the null hypothesis).
Substitute the values:

$$
LATEXBLOCK0
$$

Answer:

The test statistic for this hypothesis test is $0.41$