4.198 Testing for a Home Field Advantage in Soccer In Exercise 3.141 on page 275, 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. (509, 657) 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)?