Question

find the critical value for a right - tailed test with $\alpha = 0.01$ and $n = 75$.
a. 2.33
b. 1.96
c. 1.645
d. 2.575

Explanation:

Step1: Recall the z - table properties

For a right - tailed test with significance level \(\alpha\), the critical value \(z_{\alpha}\) is the value such that \(P(Z>z_{\alpha})=\alpha\).

Step2: Use the standard normal distribution table

Given \(\alpha = 0.01\). Looking up in the standard normal distribution table (z - table), we know that \(P(Z>z)=0.01\) implies \(P(Z\leq z)=1 - 0.01=0.99\).
From the standard normal table, the \(z\) - value corresponding to a cumulative probability of \(0.99\) is \(z = 2.33\).

Answer:

A. \(2.33\)