Hypothesis Testing and Contingency Tables (AQA A-Level Further Maths): Flashcards

$\bar{x} = \frac{\sum x_i}{n}$

$s^2 = \frac{1}{n-1}\sum(x_i - \bar{x})^2$

Bessel's correction; makes it an unbiased estimator

$\frac{s}{\sqrt{n}}$

$\bar{X} \sim N\left(\mu, \frac{\sigma^2}{n}\right)$

$\bar{x} \pm z \times \frac{s}{\sqrt{n}}$

1.96

No, only before sampling; after, $\mu$ is or isn't in interval

Decreases width (smaller standard error)

Use $s$ when population variance unknown; $\sigma$ when known