2. (5pts) Suppose that in University of California at Riverside, 28% of students are in favor of converting from the qua

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2 5pts Suppose That In University Of California At Riverside 28 Of Students Are In Favor Of Converting From The Qua 1 (125.62 KiB) Viewed 43 times

2. (5pts) Suppose that in University of California at Riverside, 28% of students are in favor of converting from the quarter to the semester system. UCR students are randomly selected and asked if they are in favor of converting to the semester system. (a) What is the smallest sample size n needed to get a good approximation of ô as a normal distribution? (b) What is the approximate distribution of ê, using the n proposed in (a)? (c) What is the approximate probability that the proportion estimate falls within one stan- dard deviation of its mean? (d) What is the exact probability that the proportion estimate falls within one standard deviation of its mean? (You can use R to calculate.) Hint: What is an equivalent event to a < p < b in terms of X where p X.? - (e) How large is the error between the approximation and the true probability?