Question

find the critical value(s) for the type of t - test with level of significance α and sample size n.
$h_a: mu
eq20, alpha = 0.01, n = 12$
a. $pm2.718$
b. $pm1.796$
c. $pm3.106$
d. $pm2.201$

Explanation:

Step1: Determine the type of t - test

Since \(H_{a}:\mu
eq20\), it is a two - tailed t - test.

Step2: Calculate the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 12\), then \(df=12-1 = 11\).

Step3: Find the critical value

For a two - tailed t - test with \(\alpha = 0.01\) and \(df = 11\), we look up the t - distribution table. The critical values are the values \(t\) such that the area in the two tails is \(\alpha=0.01\) (i.e., \(\frac{\alpha}{2}=0.005\) in each tail).
From the t - distribution table, \(t_{\frac{\alpha}{2},df}=t_{0.005,11}=3.106\)

Answer:

C. \(\pm3.106\)