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Unformatted text preview: Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science May 10 Prof. Albert R. Meyer revised May 7, 2010, 1069 minutes In-Class Problems Week 14, Mon. Problem 1. A recent Gallup poll found that 35% of the adult population of the United States believes that the theory of evolution is “well-supported by the evidence.” Gallup polled 1928 Americans selected uniformly and independently at random. Of these, 675 asserted belief in evolution, leading to Gallup’s estimate that the fraction of Americans who believe in evolution is 675 / 1928 ≈ . 350 . Gallup claims a margin of error of 3 percentage points, that is, he claims to be confident that his estimate is within 0.03 of the actual percentage. (a) What is the largest variance an indicator variable can have? (b) Use the Pairwise Independent Sampling Theorem to determine a confidence level with which Gallup can make his claim. (c) Gallup actually claims greater than 99% confidence in his estimate. How might he have ar- rived at this conclusion? (Just explain what quantity he could calculate; you do not need to carry out a calculation.) (d) Accepting the accuracy of all of Gallup’s polling data and calculations, can you conclude that there is a high probability that the number of adult Americans who believe in evolution is 35 ± 3 percent? Problem 2. Yesterday, the programmers at a local company wrote a large program. To estimate the fraction, b , of lines of code in this program that are buggy, the QA team will take a small sample of lines chosen randomly and independently (so it is possible, though unlikely, that the same line of code might be chosen more than once). For each line chosen, they can run tests that determine whether that line of code is buggy, after which they will use the fraction of buggy lines in their sample as...
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- Spring '11
- Computer Science, Probability theory, Gallup, In-class problems, Pairwise Independent Sampling