Question

find the critical value ( z_c ) that corresponds to a 99% confidence level.

a. ( pm 1.96 )
b. ( pm 1.645 )
c. ( pm 2.575 )
d. ( pm 2.33 )

Explanation:

Step1: Calculate the significance level

The confidence level \(C = 0.99\). The significance level \(\alpha=1 - C\).

$$ \alpha=1 - 0.99=0.01 $$

Step2: Find the area in the two - tails

Since it is a two - tailed test, the area in each tail is \(\frac{\alpha}{2}\).

$$ \frac{\alpha}{2}=\frac{0.01}{2}=0.005 $$

Step3: Find the \(z\) - value

We want to find \(z_c\) such that \(P(Z\lt - z_c)+P(Z\gt z_c)=\alpha\) or \(P(Z\lt z_c)=1-\frac{\alpha}{2}=0.995\). Looking up in the standard normal table (or using a calculator with a normal - distribution function), the \(z\) - value corresponding to a cumulative probability of \(0.995\) is \(z = 2.575\).

Answer:

C. \(\pm2.575\)