6.1 | Inference & Sampling Distribution of a Sample Proportion

What are the three conditions for inference of a sample proportion?

1. The sample must be random.

2. Individuals in a sample must be independent (10% rule)

3. There should be over 10 successes and over 10 failures (normality assumption)

Across many random samples of size n from a population with proportion p, the average of \hat{p} is…

Therefore, \hat{p} is an ______ of ______ in random sampling.

p

unbiased estimator, p

The standard deviation of \hat{p} is… (equation)

This shows that as n increases, \hat{p} ’s variability (increases/decreases) by (equation) proportion.

\sigma_{\hat{p}}=\sqrt{\frac{p\left(1-p\right)}{n}}

decreases, \frac{1}{\sqrt{n}}

A standard error is…

an estimate of the standard deviation of a sampling distribution

Equation of standard error

SE=\frac{s}{\sqrt{n}}

Equation of marginal error

ME=z^{*}\times\frac{\sigma}{\sqrt{n}}