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 a

Answer 1

To find the critical value for a normal distribution with a significance level (alpha) of 0.005, you first need to determine whether you are looking for a one-tailed or two-tailed test.

1. **For a one-tailed test** (where you are only interested in one side of the distribution):
- You want the z-value such that the area to the right (or left, depending on the context) of the z-value equals 0.005.
- This means you will look up the z-value that corresponds to 1 - 0.005 = 0.995 in the standard normal distribution table (or use a calculator).

2. **For a two-tailed test** (where you are interested in both extremes):
- You will split alpha into two tails, so you will use 0.005 / 2 = 0.0025 for each tail.
- This means you will look up the z-value that corresponds to 1 - 0.0025 = 0.9975 in the standard normal distribution table.

### Calculation:

Using a standard normal distribution table or calculator:

- For a one-tailed test at alpha = 0.005:
- The critical z-value \( z \) is approximately **2.576** (since 0.995 corresponds to the area to the left of the z-value).

- For a two-tailed test at alpha = 0.005:
- The critical z-value \( z \) is approximately **±2.576** (you need to consider both the positive and negative ends).

### Summary:
- **One-tailed test critical value**: \( z \approx 2.576 \)
- **Two-tailed test critical values**: \( z \approx -2.576 \) and \( z \approx 2.576 \)

If you specify if you need a one-tailed or two-tailed critical value, I can provide further details or confirmation.