Question

find the critical value ( t_{c} ) for the confidence level ( c = 0.99 ) and sample size ( n = 12 ).
click the icon to view the t - distribution table.
( t_{c}=square ) (round to the nearest thousandth as needed.)

Explanation:

Step1: Calculate the degrees of freedom

Degrees of freedom \( df=n - 1\). Given \(n = 12\), so \(df=12-1 = 11\).

Step2: Calculate the significance level \(\alpha\)

\(\alpha=1 - c\). Given \(c = 0.99\), so \(\alpha=1 - 0.99=0.01\).

Step3: Determine the tail - type

Since it is a confidence interval (two - tailed test), \(\frac{\alpha}{2}=\frac{0.01}{2}=0.005\).

Step4: Look up the \(t\) - value in the \(t\) - distribution table

Using the \(t\) - distribution table with \(df = 11\) and \(\frac{\alpha}{2}=0.005\), we find the critical value.

Answer:

\(t_{c}=3.106\)