Formula Review - Introductory Business Statistics

Formula Review

9.3 Probability Distribution Needed for Hypothesis Testing

Sample size	Test statistic
< 30 (σ unknown)	$t_{c} = \frac{\bar{X} - μ_{0}}{s / \sqrt{n}}$
< 30 (σ known)	$Z_{c} = \frac{\bar{X} - μ_{0}}{σ / \sqrt{n}}$
> 30 (σ unknown)	$Z_{c} = \frac{\bar{X} - μ_{0}}{s / \sqrt{n}}$
> 30 (σ known)	$Z_{c} = \frac{\bar{X} - μ_{0}}{σ / \sqrt{n}}$

Table 9.7 Test Statistics for Test of Means, Varying Sample Size, Population Known or Unknown

9.4 Full Hypothesis Test Examples

Test statistic for a hypothesis test of proportions:

$Z_{c} = \frac{p' - p_{0}}{\sqrt{\frac{p_{0} (1 - p 0)}{n}}}$