Question

2. Consider a sample of 46 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.

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Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A.

H0​:

p=0.5

H1​:

p>0.5

B.

H0​:

p>0.5

H1​:

p=0.5

C.

H0​:

p=0.5

H1​:

p≠0.5

D.

H0​:

p=0.5

H1​:

p<

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Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is? (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.)

___________________________________

Identify the conclusion for this hypothesis test.

A.

Fail to reject

H0.

There

is not

sufficient evidence to support the claim that the probability of the home team winning is greater than​ one-half.

B.

Reject

H0.

There

is

sufficient evidence to support the claim that the probability of the home team winning is greater than​ one-half.

C.

Reject

H0.

There

is not

sufficient evidence to support the claim that the probability of the home team winning is greater than​ one-half.

D.

Fail to reject

H0.

There

is

sufficient evidence to support the claim that the probability of the home team winning is greater than​ one-half.

Answer 1

Solution:

This a left (One) tailed test.

A)

The null and alternative hypothesis is,

Ho: p = 0.5

Ha: p > 0.5

B)

Test statistics

z = ( - ) / *(1-) / n

= ( 0.587 - 0.50) / (0.5*0.5) /46

= 1.18

P-value = P(Z > z )

= 1 - P(Z < 1.18 )

= 0.119

The p-value is p = 0.119 , and since p = 0.119 > 0.01, it is concluded that the null hypothesis is not rejected.

A)

Fail to reject H0.

There is not sufficient evidence to support the claim that the probability of the home team winning is greater than​ one-half.