Question

Consider a sample of

51

football​ games, where

30

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 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.)

Answer 1

Solution :

The null and alternative hypothesis is

H0 : p = 0.5

Ha : p > 0.5

= x / n = 30 / 51 = 0.59

P0 = 0.5

1 - P0 = 1 - 0.5 = 0.5

= 0.01

Test statistic = z =

= - P0 / [P0 * (1 - P0 ) / n]

= 0.59 - 0.5 / [(0.5 * 0.5) / 51 ]

Test statistic = z = 1.29

This is the right tailed test .

P(z > 1.29) = 1 - P(z < 1.29) = 1 - 0.902

P-value = 0.098