Question

Consider a sample of 50 football​ games, where 33 of them were won by the home team. Use a 0.05 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. Upper H 0 ​: pequals 0.5Upper H 1 ​: pless than 0.5 B. Upper H 0 ​: pequals 0.5Upper H 1 ​: pgreater than 0.5 C. Upper H 0 ​: pgreater than 0.5Upper H 1 ​: pequals 0.5 D. Upper H 0 ​: pequals 0.5Upper H 1 ​: pnot equals 0.5 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is nothing . ​(Round to two decimal places as​ needed.) Identify the​ P-value for this hypothesis test. The​ P-value for this hypothesis test is nothing . ​(Round to three decimal places as​ needed.) Identify the conclusion for this hypothesis test.

Answer 1

The Hypotheses ate:

Ho: p=0.50

Ha : p>0.50

Rejection region:

Reject Ho if Z >Z _0.05 =1.645

The sample proportion is calculated as

Test statistic:

P-value:

The P-value is computed using Z table shown below as

P-value=0.012

Conclusion:

Since the P-value < 0.05 and Z > Z_0.05 , hence we can reject the null hypothesis and conclude that there is sufficient evidence to support the claim.

Z table: