# Errors for two-sided hypotheses

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?