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
(round to two decimal places as needed. use a comma to separate answers as needed.)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(round to two decimal places as needed.)
a. the rejection region is z <

b. the rejection region is z >

c. the rejection regions are z < - 2.17 and z > 2.17.
choose the correct graph of the rejection region below.

Explanation:

Step1: Determine the significance level for each tail

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

Step2: Find the critical z - values

We look up the z - score in the standard normal distribution table (or use a calculator with a normal distribution function) such that the area to the left of \(z_1\) is \(0.015\) and the area to the right of \(z_2\) is \(0.015\).
Using a standard normal table or a calculator (e.g., \(z=\text{NORMSINV}(0.015)\) in Excel), we find that \(z=- 2.17\) (for the left - tail) and \(z = 2.17\) (for the right - tail) since the standard normal distribution is symmetric about \(z = 0\)

Step3: Define the rejection regions

The rejection regions for a two - tailed test are \(z z_{2}\). Substituting \(z_{1}=-2.17\) and \(z_{2}=2.17\), the rejection regions are \(z < - 2.17\) and \(z>2.17\)

Answer:

The critical values are \(-2.17,2.17\) and the rejection regions are \(z < - 2.17\) and \(z>2.17\). The correct graph is the one (presumably option B in the graph choices, although the actual graph content is not fully described in text but based on the two - tailed nature with two shaded tails) that has two shaded tails in the standard normal distribution curve, one on the left of \(z=-2.17\) and one on the right of \(z = 2.17\)