Question

ch 17* you are testing $h_0: mu = 0$ against $h_a: mu > 0$ based on an srs of 20 observations from a normal population. what values of the z - statistic are statistically significant at the $alpha = 0.005$ level? (hint: p - values that are smaller than alpha.)
all values for which $z > 2.81$.
all values for which $|z| > 2.81$.
all values for which $z > 2.576$

Explanation:

Step1: Recall one - sided z - test critical value concept

For a one - sided z - test with significance level $\alpha = 0.005$, we look up the z - value in the standard normal distribution table.

Step2: Find the critical z - value

The critical z - value for a right - tailed test with $\alpha=0.005$ is such that $P(Z > z_{\alpha})=\alpha$. Looking up in the standard normal table, the critical z - value $z_{0.005}=2.81$. In a one - sided test $H_a:\mu>0$, the rejection region is for $z > 2.81$.

Answer:

All values for which $z > 2.81$.