Question

If you want to construct a 90% confidence interval, what critical value (z*) should you use? Group of answer choices 2.576 1.960 1.645 2.221

Answer 1

For this case we know that the confidence level is 90% so then the significance level is
`\alpha=1-0.9 =0.1` and
`\alpha/2 =0.05`. And we can find in the normal standard distribution a value who accumulates 0.5 of the area on each tail and we got:

`z_(\alpha/2)= \pm 1.645`

And the best option would be:

1.645

Explanation:

We assume that the parameter of interest is
`\theta` and we can assume that the distribution for this parameter is normally distributed so then the confidence interval assuming a two sided interval is given by:

`\hat \theta \pm z_(\alpha/2) SE`

Where
`\hat \theta` represent the estimator for the parameter, SE the standard error and
`z_(\alpha/2)` the critical value.

For this case we know that the confidence level is 90% so then the significance level is
`\alpha=1-0.9 =0.1` and
`\alpha/2 =0.05`. And we can find in the normal standard distribution a value who accumulates 0.5 of the area on each tail and we got:

`z_(\alpha/2)= \pm 1.645`

And the best option would be:

1.645