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

Answer:

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

Step-by-step 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