This is a practice exam from my professor - is there any reason n in the test statistic equation would be 50 not 200? Is this a typo or am I missing something!

5. One sample Cl for p. A real estate company in Los Angeles is considering adding an office in Malibu. Before making the final decision to move, they ask you to estimate a range of reasonable values for the proportion of Malibu home owners planning to sell their home in the next year. You randomly sample 200 Malibu homeowners and find that 40 plan to sell their home in the next year. (a) What is the best estimate for the proportion of homeowners that plan to sell their homes in the next year? (b) Construct a 90% confidence interval for the population proportion of homeowners that plan to sell their homes in the next year. Interpret this interval. (c) The owner of the real estate company thinks the actual population proportion is 15%. Does the data support this belief? Explain. (d) The owner wants the confidence interval length to be no more than 5%. How many homeowners must be sampled to ensure this happens? (a) p = 40/200 = 0.20 (b) p E (0. 14, 0.26) 1 # 200 . > qnorm (0 . 10/2) [1] -1. 645 p(1 - p) 0.2(1 - 0.2) pepiza/2 = 0.20 + 1.645 n 50 = 0.20 + 0.06 = (0.14, 0.26)