Part BCSIR NET December 2024invert-the-bias-factor-not-the-variance

Invert the bias factor not the variance

Let P be the population proportion of units possessing a certain attribute in a population of N units. Let p be the sample proportion in a simple random sample (without replacement) of n units, (2 ≤ n < N). Then an unbiased estimator of P(1 − P) is

A.((N − n)/(Nn))p(1 − p)
B.((N − n)/((N − 1)n))p(1 − p)
C.(n/(n − 1))p(1 − p)
D.(((N − 1)n)/(N(n − 1)))p(1 − p)✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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Invert the bias factor not the variance

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