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 0.71
(round to two decimal places as needed.)
identify the p - value for this hypothesis test
the p - value for this hypothesis test is
(round to three decimal places as needed.)

Explanation:

Step1: Determine the type of test

Since the claim is that the probability that the home team wins is greater than one - half ($p>0.5$), this is a right - tailed test.

Step2: Use the formula for the P - value in a right - tailed z - test

For a right - tailed z - test, the P - value is $P(Z > z)$, where $z$ is the test statistic. Given $z = 0.71$.
We know that $P(Z>0.71)=1 - P(Z\leq0.71)$. From the standard normal table, $P(Z\leq0.71)=0.7611$.
So, $P(Z > 0.71)=1 - 0.7611=0.239$

Answer:

The P - value for this hypothesis test is $0.239$