Question

Anyone who plays or watches sports has heard of the "home field advantage." Teams tend to win more often when they play at home. Or do they? If there were no home field advantage, the home teams would win about half of all games played. During the 2010 season, the home team won 142 of the 250 regular-season football league games. At a 3% level of significance, is there strong evidence of a home field advantage in professional football?

Required:
a. State the null and alternative hypotheses in both words and math notation. Will you perform a left-tailed, right-tailed, or two-tailed test?
b. Calculate the sample proportion. Is the sample proportion consistent with your alternative hypothesis?
c. Sketch the sampling distribution and label the mean, standard error, and the observed sample statistic. Calculate the test statistic. Is the test statistic unusual? Use the test statistic to find the P-value

Answer 1

H0 : μ = 0.5

H0 : μ > 0.5

Kindly check explanation

Explanation:

H0 : μ = 0.5

H0 : μ > 0.5

We perform a right tailed test :

Sample proportion :

Number of games won, x = 142

Number of games, n = 250

phat = x / n = 142 / 250 = 0.568 = 56.8%

Yes, it is consistent

Test statistic :

(phat - p) * √Phat(1-Phat)/n

1 -Phat = 1 -0.568 = 0.432

(0.568 - 0.5) /√(0.568*0.432)/250

0.068 / 0.0313289

= 2.17

The Pvalue using the z test statistic :

Pvalue = 0.015

α = 0.03

Since ;

Pvalue < α ; We reject the null and conclude that teams tend to win more often when they play at home.