Question: Trying to understand p-value and critical value approach to hypothesis test for a proportion. In this question, p'=.42 and p 0 = .4, critical value

Trying to understand p-value and critical value approach to hypothesis test for a proportion.

In this question, p'=.42 and p0 = .4, critical value is 1.41 (right-tail test). The level of significance is .08.

Critical Value Approach:

(.42-.4)/ ((.4*.6)/200) = .57735

.58<1.41, so the null hypothesis is rejected.

However, if the p-value is .281 (from .58 on the z-table) and .281 > alpha (.08), the null hypothesis fails to be rejected, right?

This doesn't make sense to me, because I'm expecting both approaches to yield the same response. Am I missing something?

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