Question

Find the critical value, assuming that the normal distribution applies.

Alpha = 0.005

a)

b)

c)

d)

e)

f)

The critical value(s) is
[ Select ]

Answer 1

To find the critical value for a normal distribution at an alpha level of 0.005, we need to determine whether the context is a one-tailed or two-tailed test, as this affects how we find the critical value.

1. **One-tailed Test**: If you're conducting a one-tailed test (testing in one direction), you would look for the critical value in the upper tail of the distribution. This means we want to find \( Z_{\alpha} \) where \( \alpha = 0.005 \).

2. **Two-tailed Test**: If it’s a two-tailed test (testing in both directions), you need to split the alpha level between the two tails. So, you would look for \( Z_{\alpha/2} \) where \( \alpha/2 = 0.0025 \) for each tail.

### Steps to find Z-critical values:

- Use the Z-table (or a standard normal distribution calculator) to find \( Z \) such that the area to the right is equal to \( \alpha \) for a one-tailed test or \( \alpha/2 \) for a two-tailed test.

- For a one-tailed test at \( \alpha = 0.005 \):
- The critical value \( Z_{0.005} \) (the value where the area to the right is 0.005) is approximately \( Z = 2.576 \).

- For a two-tailed test at \( \alpha = 0.005 \):
- You would look for \( Z_{0.0025} \) (the value where the area to the right is 0.0025), which is also approximately \( Z = 2.807 \).

### Summary:

- **One-tailed critical value at \( \alpha = 0.005 \)**: \( Z \approx 2.576 \)
- **Two-tailed critical value at \( \alpha = 0.005 \)**: \( Z \approx \pm 2.807 \)

You may choose from these values based on the context of your test. If you need a specific answer, please clarify whether it is a one-tailed or two-tailed test.