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?

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Possible Answers

Type I: There is a difference in proportions, but the observed difference is not big enough to indicate that the proportions are different.
Type II: There is not a difference in proportions, but the observed difference is large enough to indicate that the proportions are different.
press1
Type I: There is not a difference in proportions, and the observed difference is not big enough to indicate that the proportions are different.
Type II: There is a difference in proportions, and the observed difference is large enough to indicate that the proportions are different.
press2
Type I: There is not a difference in proportions, but the observed difference is big enough to indicate that the proportions are different.
Type II: There is a difference in proportions, but the observed difference is not large enough to indicate that the proportions are different.
press3
Type I: There is a difference in proportions, and the observed difference is big enough to indicate that the proportions are different.
Type II: There is not a difference in proportions, and the observed difference is not large enough to indicate that the proportions are different.
press4