Question

Suppose that you want to conduct a left-handed hypothesis test at $5\%$significance level. How much the critical value be chosen?

Short answer

The critical value to be chosen is $-1.645$.

Step-by-step solution

Step 1. Finding the critical value

If the null hypothesis is true, the probability equals to $0.05$that the test statistic will fall in the rejection region, in this case, to the left of the critical value.

The critical value for a left-tailed test are $-z_{\alpha }$. By using the standard normal tables we find the critical values. Because $\alpha =0.05$, the critical value is $-z_{0.05}=-1.645$is shown in the figure below.