30. A Statistics instructor is curious in knowing the true proportion of students at the college who use a Macintosh product on a regular basis. At the beginning of Fall 2021 the instructor surveyed her 67 students and found that 35 used a Mac. We will treat the 67 students as a simple random sample. a. [2] Identify the following: x = n = p = b. [1] Which distribution should you use for this problem? (circle the correct answer) Normal Distribution t-Distribution c. Find a 90% confidence interval for the true population proportion of students at MJC who use a Mac. [3] Solution A Identify values to plug into the formula p + (za) p(1-p) n Write solution first as p + EBP: Write solution in interval notation: (_ [1] Solution B Check your "by hand" work by running the appropriate test in the calculator: [2] Interpretation 31. [4] If the same professor wanted to be MORE confident, say 97%, AND wanted a smaller error bound, say within 5%, how many students would she need to survey? (go ahead and use the previously calculated point-estimate instead of p'=0.5)