Question

I Use the figure for the first 2 questions C O NIR 1-a 을 -2a/2 0 a/2 1) Determine the right critical value for a 95% confidence interval for a two-tailed decision, denoted as Zal2 in the figure 2) Determine the left critical value for a 95% confidence interval for a two-tailed decision, denoted as - Za/2 in the figure

Answer 1

Here confidence interval is 95%

It means $\alpha=1-0.95=0.05$

P(Z > 2/2) = a/2

$0.5-P(0<Z<z_{\alpha/2})=0.025$

$P(0<Z<z_{\alpha/2})=0.5-0.025$

$P(0<Z<z_{\alpha/2})=0.475$

In the normal table search for 0.475 then see the value z this value of z = 1.96 is the right critical value for a 95% confidence interval for a two tailed decision.

Now

$P(Z<-z_{\alpha/2})=0.025$

But we know that standard normal curve is symmetric about zero it means area to the left of a point -z is equal to the area to the right of the point z.

Therefore

We get the left critical value for a 95% confidence interval for a two tailed decision is -1.96.