Simple Random Sampling in Statistics | Definition & Examples
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Simple Random Sampling: 6 Basic Steps With Examples
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2.3 (Simple Random Sampling With Replacement (Part (ii))) (a) Show that Z is an unbiased estimator of μ with V(Z) given in (2.3). Hint: Find V(Zk) first. (b) Let Ym and Z be the two versions of the sample mean under SRSWR and assume that n ≥ 2 and σ^2 > 0. Show that V(ym) > V(μ) and V(z) > V(μ), where μ is the population mean, with the sample of size n selected by SRSWOR. Let Yi be the number of times that unit i is selected under SRSWR, 1 ≤ i ≤ N. We can rewrite Z as Z = ∑(Yi / n)
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With and without replacement. In the following situations assume that half of the specified population is male and the other half is female. (a) Suppose you're sampling from a room with 10 people. What is the probability of sampling two females in a row when sampling with replacement? What is the probability when sampling without replacement? (b) Now suppose you're sampling from a stadium with 10,000 people. What is the probability of sampling two females in a row when sampling with replacement?
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