Question

find the critical value(s) and rejection region(s) for the type of z - test with level of significance α. include a graph with your answer.
two - tailed test, α = 0.03
the critical value(s) is/are z = (round to two decimal places as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Find the area in each tail

For a two - tailed test, the significance level \(\alpha = 0.03\) is split evenly between the two tails. So the area in each tail is \(\frac{\alpha}{2}=\frac{0.03}{2}=0.015\).

Step2: Find the critical \(z\) - values

We look for the \(z\) - score such that the area to the left of \(z\) is \(1 - 0.015=0.985\) and the area to the left of \(-z\) is \(0.015\).
Using a standard normal table or a calculator with a normal distribution function (e.g., for \(P(Z\leq z)=0.985\), \(z\approx1.81\) and for \(P(Z\leq - z)=0.015\), \(z\approx - 1.81\))

Answer:

The critical values are \(z=- 1.81,1.81\)