Approximating the Distribution of the Sample Proportion (VCE SSCE Mathematical Methods): Flashcards

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Approximating the Distribution of the Sample Proportion
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Symbol for population proportion

pp

Symbol for sample proportion

p^\hat{p} or P^\hat{P}

Sample size for practical exact probability calculations

Less than 10

Condition for normal approximation of sample proportion

np>5np > 5 and n(1p)>5n(1-p) > 5

Mean of sample proportion distribution

μ=p\mu = p

Standard deviation of sample proportion

σ=p(1p)n\sigma = \sqrt{\frac{p(1-p)}{n}}

Shape of sample proportion distribution (large nn)

Approximately normal

Why sample proportions vary between samples

Natural consequence of random sampling

Centre of sample proportion distribution

Population proportion pp

What mean of sample proportions estimates

Population proportion

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