Question

In: Statistics and Probability

Let p be the (unknown) true fraction of voters who support a particular candidate A for office.

 

6. Let p be the (unknown) true fraction of voters who support a particular candidate A for office. To estimate p, we poll a random sample of n voters. Let Fn be the fraction of voters who support A among n randomly selected voters.

A. Using Chebyshev’s Inequality, calculate an upper bound on the probability that if we poll 100 voters, our estimate Fn differs from p by more than 0.1. (Hint: you may need to use the fact that x(1 − x) ≤ 1/4 for any 0 ≤ x ≤ 1).

B. How many voters need to be polled if we want to have high confidence (probability at least 95%) that our estimate differs from p by at most 0.01? Use Chebyshev’s Inequality.

7. Repeat question 6 using the Central Limit Theorem to calculate probabilities

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Expert Solution

orchestra answered 2 years ago
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