Question

the p - value for a hypothesis test turns out to be 0.03877. at a 1% level of significance, what is the proper decision?
reject $h_0$
fail to reject $h_0$

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Explanation:

Step1: Recall decision - rule

In hypothesis testing, if p - value $\leq\alpha$ (level of significance), we reject $H_0$. If p - value $>\alpha$, we fail to reject $H_0$.

Step2: Compare p - value and $\alpha$

Given p - value = 0.03877 and $\alpha=0.01$. Since 0.03877 > 0.01.

Answer:

Fail to reject $H_0$