Question

find the critical value for a two - tailed test with $\alpha=0.01$ and $n = 30$.
a. $\pm1.96$
b. $\pm1.645$
c. $\pm2.33$
d. $\pm2.575$

Explanation:

Step1: Determine the significance level for each tail

For a two - tailed test, the significance level \(\alpha = 0.01\) is split equally between the two tails. So, \(\frac{\alpha}{2}=\frac{0.01}{2}=0.005\).

Step2: Look up the z - value in the standard normal distribution table

We want to find the \(z\) - value such that the area to the right of \(z\) is \(0.005\) and the area to the left of \(-z\) is \(0.005\).
Looking up in the standard normal distribution table (or using a calculator with a normal - distribution function), the \(z\) - value corresponding to an area of \(1 - 0.005=0.995\) (since the total area under the standard normal curve is \(1\)) is \(z = 2.575\).

Answer:

D. \(±2.575\)