Question

Consider a sample of 46 football​ games, where 26 of them were won by the home team. Use a 0.10 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.

H=

Identify P value

p=

P=

Answer 1

Solution:

Given:

Sample size = n = 46

x = Number of football games were won by the home team = 26

Level of significance = 0.10

Claim:  the probability that the home team wins is greater than​one-half.

Step 1) State H₀ and H₁:

H₀: p = 0.5 Vs H₁: p > 0.5

Right tailed test

Step 2) Test statistic:

where

thus

Step 3) P-value:

For right tailed test ,P-value is:

P-value = P(Z > z test statistic)

P-value = P(Z > 0.88 )

P-value = 1 - P(Z < 0.88 )

Look in z table for z = 0.8 and 0.08 and find corresponding area.

P( Z< 0.88 ) = 0.8106

thus

P-value = 1 - P(Z < 0.88 )

P-value = 1 - 0.8106

P-value = 0.1894

Step 4) Decision Rule:
Reject null hypothesis H0, if P-value < 0.10 level of significance, otherwise we fail to reject H0

Since P-value = 0.1894 > 0.10 level of significance, we fail to reject H0

Step 5) Conclusion:

At 0.10 level of significance, we do not have sufficient evidence to support the claim that: the probability that the home team wins is greater than​one-half.