Question

Consider a sample of

48

football games, where

25

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 0H0 :

pequals=0.5

Upper H 1H1 :

pnot equals≠0.5

B.

Upper H 0H0 :

pgreater than>0.5

Upper H 1H1 :

pequals=0.5

C.

Upper H 0H0 :

pequals=0.5

Upper H 1H1 :

pgreater than>0.5

Your answer is correct.

D.

Upper H 0H0 :

pequals=0.5

Upper H 1H1 :

pless than<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 p-values

Answer 1

Solution :

Given that,

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.5

Ha: p 0.5

Option c is correct.

= 0.5

1 - = 1 - 0.5 = 0.5

n = 48

x = 25

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 25 / 48 = 0.52

Test statistics

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

= ( 0.52 - 0.5) / (0.5*0.5) / 48

= 0.29

P-value = P(Z>z)

= 1 - P(Z <z )

= 1- P(Z < 0.29)

= 1 - 0.6141

= 0.3859

The p-value is p = 0.3859 and since p = 0.3859 ≥ 0.05, it is concluded that the null hypothesis is not rejected.