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In order to estimate f, the true fraction of smokers in a large population, Alvin selects n people at random. His estimator M, is obtained by dividing Sa, the number

of smokers in his sample, by N, i.e., M = Sn/n. Alvin chooses the sample size n to be the smallest possible number for which the Chebyshev inequality yields a guarantee that P(|M, - f|2) < 8, where e and ó are some pre specified tolerances. Determine how the value of n recommended by the Chebyshev inequality changes in the following case ) The value of e is reduced to half its original value. The value of ó is reduced to half its original value.

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