Unit 6 | All Categorical Data Formulas

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General Confidence Interval Formula

(General form for all confidence intervals)

(statistic) \pm (critical\ value)(SE)

Confidence interval for single population proportion

\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}

Confidence interval for difference between two proportions

(\hat{p}_1 - \hat{p}_2) \pm z^* \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}

General significance test (general form for all hypothesis tests)

test\ statistic = \frac{(statistic) - (parameter)}{SE}

Test for single population proportion against hypothesized value (one-proportion z-test)

z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}

Test for difference between two population proportions (two-proportion z-test)

z = \frac{(\hat{p}_1 - \hat{p}_2) - 0}{\sqrt{\hat{p}_c(1-\hat{p}_c)\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}}

Pooled sample proportion (combined proportion when testing equality of two proportions)

\hat{p}_c = \frac{x_1 + x_2}{n_1 + n_2}