Answer each of the following questions completely. All work and steps should be shown, think of this as proving to me you understand the process. When possible to answer using a complete sentence and offering explanation, please do so.

ACT, Inc. reported that 74% of 1644 randomly selected college freshmen returned to college the next year.

[3 pts] Construct and interpret a 90% confidence interval to estimate the retention rate for college freshmen.



[3 pts] Let’s say they only need a 2% margin of error with the same level of confidence the following year. How many college freshmen must be surveyed?



[1 pts] If they increased their confidence level to 95%, would the confidence intervals get wider or narrower? Explain why.



[8 pts] There were 2430 Major League Baseball games played in 2009, and the home team won the game in 53% of the games. If we consider the games played in 2009 as a sample of all MLB games, test to see if there is evidence, at the 5% level, that the home team wins more than half the games. (Show all steps of the hypothesis test, including checking conditions and a graph, for full credit)