Author Question: Suppose we know that the proportion of objects in a population that have a particular characteristic ... (Read 49 times)

cyc028 · **on:** Feb 26, 2023

Suppose we know that the proportion of objects in a population that have a particular characteristic of interest is 0.10. Are there any concerns if we want to calculate probabilities for the sampling distribution of\(\style{font-family:Times New Roman;}{\widehat p}\) n= 40 using a normal approximation?

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Becausenis large, our only concern with using a normal approximation will be the small amount of variability in the sampling distribution of\(\style{font-family:Times New Roman;}{\widehat p}\).

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Because_{\(\style{font-family:Times New Roman;}{\;n}\)}is small here, the sampling distribution of\(\style{font-family:Times New Roman;}{\widehat p}\)should not be assumed to be approximately normal.

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Because\(\style{font-family:Times New Roman;}{\widehat p}\) ≤ 0.5, the sampling distribution of\(\style{font-family:Times New Roman;}{\widehat p}\)should not be assumed to be approximately normal.

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If n \(\style{font-family:Times New Roman;}{\widehat p}\) < 5, then a normal approximation is not appropriate.

dadgoere765 · **Reply #1 on:** Feb 26, 2023

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