To find the critical values for a two-tailed test with \(\alpha = 0.01\) using the normal distribution, we need to determine the z-scores that correspond to the tails of the distribution that together contain 1% of the area.
In a two-tailed test with \(\alpha = 0.01\), each tail will have an area of:
\[ \frac{\alpha}{2} = \frac{0.01}{2} = 0.005 \]
To find the critical z-values, we look for the z-scores that correspond to the cumulative area of \(1 - 0.005 = 0.995\) and \(0.005\) in the z-table.
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For the left tail (0.005):
- The corresponding z-value is approximately \(-2.576\).
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For the right tail (0.995):
- The corresponding z-value is approximately \(2.576\).
Thus, the critical values for this two-tailed test at \(\alpha = 0.01\) are:
\[ z = -2.576 \quad \text{and} \quad z = 2.576 \]
Therefore, the critical values are:
\(-2.576\) and \(2.576\).