A random sample is to be selected from a population.
For which of the following sample sizes would the sampling distribution of p̂ be approximately normal if p = 0.61?
(Select all that apply.)
n = 10
n = 20
n = 30
n = 50
n = 100
n = 200
For which of the following sample sizes would the sampling distribution of p̂ be approximately normal if p = 0.3
(Select all that apply.)
n = 10
n = 20
n = 30
n = 50
n = 100
n = 200
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For the first question, the sampling distribution of p̂ will be approximately normal for sample sizes n ≥ 10 according to the Central Limit Theorem. Therefore, the following sample sizes will have approximately normal sampling distributions: n = 10, n = 20, n = 30, n = 50, n = 100, and n = 200.
For the second question, the same reasoning applies. The sampling distribution of p̂ will be approximately normal for sample sizes n ≥ 10. Therefore, the following sample sizes will have approximately normal sampling distributions: n = 10, n = 20, n = 30, n = 50, n = 100, and n = 200.
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1) n = 30, 50, 100, 200
2) n = 50, 100, 200
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