Sometimes you'll be interested in identifying *any* difference in proportions (as opposed to one larger proportion). Consider these slightly adjusted hypotheses for the opportunity cost example:

**\(H_0\)**: Reminding students that they can save money for later purchases will not have any impact on students' spending decisions.**\(H_A\)**: Reminding students that they can save money for later purchases will*change*the chance they will continue with a purchase.

What are type I (false positive) and type II (false negative) errors for the **two-sided** hypotheses related to the opportunity costs example?

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