Question

Find the value Z a/2 needed to construct a confident
interval with the given level of 99.7%

Answer 1

The critical value is
`Z_{(\alpha)/(2)} = 2.96`

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1 - 0.997)/(2) = 0.0015`

Now, we have to find z in the Z-table as such z has a p-value of
`1 - \alpha`.

That is z with a pvalue of
`1 - 0.0015 = 0.9985`, so Z = 2.96.

The critical value is
`Z_{(\alpha)/(2)} = 2.96`