Answer:
The critical value is [tex]Z_{\frac{\alpha}{2}} = 2.96[/tex]
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.997}{2} = 0.0015[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.0015 = 0.9985[/tex], so Z = 2.96.
The critical value is [tex]Z_{\frac{\alpha}{2}} = 2.96[/tex]
