Exercise

proportions_ztest() for two samples

That took a lot of effort to calculate the p-value, so while it is useful to see how the calculations work, it isn't practical to do in real-world analyses. For daily usage, it's better to use the statsmodels package.

Recall the hypotheses.

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

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

late_shipments is available, containing the freight_cost_group column. numpy and pandas have been loaded under their standard aliases, and proportions_ztest has been loaded from statsmodels.stats.proportion.

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Get the counts of the late column grouped by freight_cost_group.