Test of two proportions

You may wonder if the amount paid for freight affects whether or not the shipment was late. Recall that in late_shipments dataset, whether or not the shipment was late is stored in the late column. Freight costs are stored in the freight_cost_group column, and the categories are "expensive" and "reasonable".

We can form hypotheses to test.

$H_{0}$: $late_{\text{expensive}} - late_{\text{reasonable}} = 0$

$H_{A}$: $late_{\text{expensive}} - late_{\text{reasonable}} > 0$

p_hats contains the estimates of population proportions (sample proportions) for the "expensive" and "reasonable" groups. ns contains the sample sizes for these groups.

Calculate the pooled sample proportion, $\hat{p}$, as the mean of p_hats weighted by ns. Use weighted.mean() or arithmetic with this equation.

$$ \hat{p} = \frac{n_{\text{expensive}} \times \hat{p}_{\text{expensive}} + n_{\text{reasonable}} \times \hat{p}_{\text{reasonable}}}{n_{\text{expensive}} + n_{\text{reasonable}}} $$

Exercise

Test of two proportions

Instructions 1/4