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old exams ... - Final Exam Summer 1994 Problem 2 In Table A...

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Final Exam -- Summer 1994 Problem 2 In Table A, Starr Vashon collects sample data a i , i = 1…12, on random variable A = the price of a line of advertising in a daily newspaper. She also records whether or not the paper was a morning edition. The sample was drawn with-out replacement from a population of 956 daily papers. A) Let π m = proportion of newspapers which are morning editions. 1) Compute a 95% confidence interval estimate of π m . From _0_ to 0.4496 ± n z p 2 1 025 . 2) If you wanted to be 90% sure that your estimate of π m differed from the true value by no more than 0.04, how big a sample would you need? n* = 235 = 2 05 . ) 1 ( ˆ - δ p p z B) Assume A ~ N(μ, σ 2 ). Compute an 80% confidence interval estimate of μ a . From 11.66 to 16.18 12 99 . 32 363 . 1 92 . 13 ) ( ˆ 10 . ± = ± A E S t A Problem 3 W = weight of any given San Diego zoo scientists equipped with tranquilizer guns and DNA testing equipment. W ~ N(210, 49). A helicopter will carry 4 randomly selected zoo scientists into the bush country of Zimbabwe to chase rhinos. It cannot make the trip if the weight of the 4 zoologists exceeds 872 pounds. What is the probability that the chopper will be overloaded? Probability = 0.011 or 1.1% = Pr(ΣW > 872) = ) 29 . 2 Pr( 4 7 210 218 Pr 4 872 Pr = - = z Z W Problem 4 Rodney Random is studying the distribution of random variable D = annual dividend income of retired heads of households.

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