Question
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 ]
Two-tailed test, alpha = 0.01
a)
b)
c)
d)
e)
f)
The critical value(s) is
[ Select ]
Answers
GPT-4o mini
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 \(2.576\).
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 \(2.576\).