Revision sheet

Sampling variability

• Statistics vary from sample to sample.
• Sampling distribution: a statistic over all samples.
• Larger $n$: less variability.

Watch out: data distribution vs sampling distribution.

Sampling distribution of p̂

$\mu = p$, $\sigma = \sqrt{p(1 - p)/n}$; normal if $np, n(1 - p) \ge 10$.

Watch out: proportion, not count.

Sampling distribution of x̄

$\mu_{\bar{x}} = \mu$, $\sigma_{\bar{x}} = \sigma/\sqrt{n}$.

Watch out: divide by $\sqrt{n}$, not $n$.

Central limit theorem

Large $n$: $\bar{x}$ approximately normal, whatever the population.

Watch out: it is about means, not about the data.

Differences

Independent samples: means subtract, variances add.

Watch out: paired data are not independent.

Bias and variability

• Unbiased: centered on the parameter.
• Variability: shrinks with $n$.
• 10% condition for independence.

Watch out: large does not mean unbiased.