Question

find the critical value for a right - tailed test with \\( \alpha = 0.01 \\) and \\( n = 75 \\).

oa. 2.33
ob. 1.96
oc. 1.645
od. 2.575

Explanation:

Step1: Determine the distribution

Since \(n = 75\) (\(n\geq30\)), we can use the standard normal distribution (\(Z -\)distribution) for hypothesis - testing.

Step2: Use the property of the standard normal distribution

For a right - tailed test with significance level \(\alpha=0.01\), we need to find the \(z\) - value such that \(P(Z>z)=\alpha = 0.01\).
Using the property \(P(Z > z)=0.01\), then \(P(Z\leq z)=1 - 0.01=0.99\).
Looking up the \(z\) - value in the standard normal distribution table (or using a calculator with a normal - distribution function, e.g., for a TI - 84: invNorm(0.99,0,1)), we find that the \(z\) - value corresponding to a cumulative probability of \(0.99\) is \(z = 2.33\).

Answer:

A. \(2.33\)