Question

find the critical value ( z_{c} ) necessary to form a confidence interval at the level of confidence shown below.
( c = 0.82 )
( z_{c}=)
(round to two decimal places as needed.)

Explanation:

Step1: Calculate the significance level $\alpha$

The confidence level is \(c = 0.82\). The significance level \(\alpha=1 - c\). So, \(\alpha=1 - 0.82=0.18\).

Step2: Calculate \(\frac{\alpha}{2}\)

\(\frac{\alpha}{2}=\frac{0.18}{2}=0.09\).

Step3: Find the \(z -\)score

We want to find \(z_{c}\) such that \(P(Z>z_{c})=\frac{\alpha}{2}=0.09\), or equivalently \(P(Z\leq z_{c})=1 - 0.09 = 0.91\). Using a standard normal table (or a calculator with a normal - distribution function, e.g., in Excel =NORM.S.INV(0.91) or in R qnorm(0.91)), we find \(z_{c}\approx1.34\).

Answer:

\(1.34\)