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Exercise

Test of two proportions

You may wonder if the amount paid for freight affects whether or not the shipment was late. Recall that in the 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".

The hypotheses to test, with "late" corresponding to the proportion of late shipments for that group, are

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

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

p_hats contains the estimates of population proportions (sample proportions) for each freight_cost_group:

freight_cost_group  late
expensive           Yes     0.082569
reasonable          Yes     0.035165
Name: late, dtype: float64

ns contains the sample sizes for these groups:

freight_cost_group
expensive     545
reasonable    455
Name: late, dtype: int64

pandas and numpy have been imported under their usual aliases, and norm is available from scipy.stats.

Instructions 1/4

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  • Calculate the pooled sample proportion, \(\hat{p}\), from p_hats and ns.

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