Download Statistics Solutions: Refusal Rates, Probabilities, and Confidence Intervals - Prof. James and more Exams Statistics in PDF only on Docsity! Page 1 of 4 Statistics 31, Section 1, Midterm II Solution Tuesday, April 12, 2005 Name: ________________Solution_______________________________ Pledge: I have neither given nor received aid on this examination. Signature: _____________________________________________________ Instructions: Do not do any actual numerical calculations. Answers in a form that you would type into an Excel field, such as “=28*SQRT(82)^2”, with a working answer, are expected. 1. In a study of the rate of refusals in telephone surveys, random telephone calls were made to ask about the next election. In some calls the interviewer gave here name, and in others both her name and the university she represented. For each call, she also offered, or did not offer, to send a copy of the final results to the person being interviewed. For the group where both the university was identified, and the results were offered, the refusal rate was 50%, which seemed to a substantial improvement over the historical refusal rate of 80% a. What are the experimental units? Individuals who were called b. What are the factors? University information, offer of sending results. c. What are the treatments? Giving university info or not, Offering results or not. d. What are the response variables? Whether or not the interview was refused e. Is the number 50% a parameter or a statistic? Statistic Page 2 of 4 2. In a study of land use in Canada, every acre is assigned to be either “pasture”, “forest”, or “neither”. Suppose that 40% of the acres are forested, and 10% are pasture. For a randomly chosen acre, what is the probability that: a. The acre is not forested? P{not F} = 1 – P{F} = 1 – 0.4 = 0.6 b. The acre is either pasture or forested? P{P or F} = P{P} + P{F} – P{P and F} = 0.4 + 0.1 – 0 = 0.5 c. The acre is neither pasture nor forested? P{neither} = 1 – P{P or F} = 1 – 0.5 = 0.5 3. When a telemarketing company calls at random, 60% of calls are not completed, while 25% are completed to a man, and 15% are completed to a woman. After that, 10% of the men, and 20% of the women buy something. a. What percent of the calls result in a sale? P{S} = P{(S & M) or (S & W)} = P{S & M} + P{S & W} – P{(S & M) and(S & W)} = P{S|M}P{M} + P{S|W}P{W} = 0.1 * 0.25 + 0.2 * 0.15 b. What percent of the sales are made to a man? P{M|S} = P{S|M}P{M} / P{S} = 0.1 * 0.25 / (0.1 * 0.25 + 0.2 * 0.15)
