Several years ago, ballots in Champaign-Urbana contained the following question to assess public opinion on an issue: "Should the State of Illinois legalize and regulate the sale and use of marijuana in a similar fashion as the State of Colorado?" Suppose that we would like to understand Champaign-Urbana's opinion on marijuana legalization. Your friend claims that among people she talks to, at least three out of every five people support legalization. To satisfy your curiosity, we obtain a random sample of 120 Champaign-Urbana residents and find that 87 support marijuana legalization. (a) State the null and alternative hypotheses, calculate the test statistic, and provide the p- value. (b) Using a level of significance of a= 0.01, make a decision about the null hypothesis and provide a concluding statement in the context of this situation. (c) In Homework 10, you constructed a 99% (two-sided) confidence interval for the true proportion of Champaign-Urbana residents who support legalizing marijuana. Using that as evidence for the hypothesis test in part a, do you come to the same conclusion that you did in part b? Explain