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.