Question

consider a sample of 50 football games, where 31 of them were won by the home team. use 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 1.70 (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

This is a right - tailed test because the claim is that \(p>0.5\).

Step2: Calculate the P - value

For a right - tailed z - test, the P - value is \(P(Z > z)\), where \(z = 1.70\).
Using the standard normal distribution table or a calculator, \(P(Z>1.70)=1 - P(Z\leq1.70)\).
From the standard normal table, \(P(Z\leq1.70) = 0.9554\).
So, \(P(Z > 1.70)=1 - 0.9554=0.045\) (rounded to three decimal places).

Answer:

\(0.045\)