Exercise 2 Last year, ballots in Champaign-Urbana contained the following questi
ID: 3318785 • Letter: E
Question
Exercise 2 Last year, 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 2017 opinion on marijuana legalization. To satisfy our curiosity, we obtain a random sample of 120 Champaign-Urbanians and find that 87 support marijuana legalization. (a) Calculate the test statistic for the test H0 : p 0.70 versus H1 : p > 0.70 where p is the true proportion of Champaign-Urbanians that support marijuana legalization. Report your answer rounded to two decimal places (b) Calculate the (approximate, using z) p-value for the test H0 : p 0.70 versus H1: p > 0.70 (c) Calculate the exact p-value for the test Ho : p = 0.70 versus H1 : p > 0.70. That is, calculate the probability of seeing as many supporters as observed, or more, assuming the null hypothesis is true. Some useful code Excel: BINOM.DIST(x, n, p, 1) gives the probability of less than or equal to x R: pbinom(x, n, p) gives the probability of less than or equal to xExplanation / Answer
pcap = 87/120 = 0.725
SE = sqrt(0.7*0.3/120) = 0.0418
test statistics, z = (0.725 - 0.7)/0.0418 = 0.5981
p-value = 0.2749
exact p-value = 0.24506601 (=1- BINOM.DIST(87,120,0.7,TRUE))
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