Do you reject a one-sided test at z = 1.5?

Question

A one-sided (upper-tail) z-test produces a test statistic of $z = 1.5$ . The critical value at the 5% level is $z_{0.05} = 1.645$ .

Do you reject the null hypothesis at the 5% level, and roughly what is the one-sided p-value?

Accepted Answer

The rule for an upper-tail test: reject H0 if z exceeds the critical value 1.645. Here z = 1.5 < 1.645, so we fail to reject H0. The one-sided p-value is 1 - \Phi(1.5) = 1 - 0.9332 = 0.0668, which is above 0.05, confirming the decision. Takeaway. For a one-sided test the entire 5% sits in one tail, giving the lower cutoff 1.645 (versus 1.96 two-sided). A statistic of 1.5 still falls short, so the result is not significant, and its p-value of about 0.067 agrees.

Do you reject a one-sided test at z = 1.5?

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