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.
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