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.
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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).
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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:
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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).
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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.