In Exercise 3.108 on page 215, we see that the home team was victorious in 70 games out of a sample of 120 games in the FA premier league, a football (soccer) league in Great Britain. We wish to investigate the proportion p of all games won by the home team in this league.

(a) Use StatKey or other technology to find and interpret a 90% confidence interval for the proportion of games won by the home team.

(b) State the null and alternative hypotheses for a test to see if there is evidence that the proportion is different from 0.5.

(c) Use the confidence interval from part (a) to make a conclusion in the test from part (b). State the confidence level used.

(d) Use StatKey or other technology to create a randomization distribution and find the p-value for the test in part (b).

(e) Clearly interpret the result of the test using the p-value and using a 10% significance level. Does your answer match your answer from part (c)?

(f) What information does the confidence interval give that the p-value doesn’t? What information does the p-value give that the confidence interval doesn’t?

(g) What’s the main difference between the bootstrap distribution of part (a) and the randomization distribution of part (d)?

Exercise 3.108

Is there a home field advantage in soccer? We are specifically interested in the Football Association (FA) premier league, a football (soccer) league in Great Britain known for having especially passionate fans. We took a sample of 120 matches (excluding all ties) and found that the home team was victorious in 70 cases.