Find the critical value(s), assuming that the normal distribution applies.

Two-tailed test, alpha = 0.01

a)

b)

c)

d)

e)

f)

The critical value(s) is
[ Select ]

1 answer

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.

  1. For the left tail (0.005):

    • The corresponding z-value is approximately \(-2.576\).
  2. 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 \(2.576\).