Do you reject when z = 2.3 at the 5% level?

Question

A two-sided z-test produces a test statistic of z = 2.3. The critical value at the 5% level is 1.96. Do you reject the null hypothesis at the 5% level, and roughly what is the two-sided p-value?

Accepted Answer

The rule for a two-sided test: reject H0 if the statistic lies beyond the critical value, i.e. if z 1.96. Here z = 2.3 1.96, so reject H0. The two-sided p-value is 2\,[1 - \Phi(2.3)] = 2(1 - 0.9893) = 2(0.0107) \approx 0.021, which is below 0.05, confirming the decision. Takeaway. The critical-value rule and the p-value rule always agree: z beyond 1.96 is the same event as a two-sided p-value below 0.05. Either way, a statistic of 2.3 rejects at the 5% level.

Do you reject when z = 2.3 at the 5% level?

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