Question

find the critical value $t_{c}$ for the confidence level $c = 0.99$ and sample size $n = 7$.
click the icon to view the t - distribution table.
$t_{c}=\square$ (round to the nearest thousandth as needed.)

Explanation:

Step1: Calculate the degree of freedom

The degree of freedom \(df=n - 1\). Given \(n = 7\), then \(df=7-1 = 6\).

Step2: Calculate the significance level

The significance level \(\alpha=1 - c\). Given \(c = 0.99\), then \(\alpha=1 - 0.99=0.01\). And \(\frac{\alpha}{2}=\frac{0.01}{2}=0.005\).

Step3: Find the critical value from t - distribution table

Looking up the \(t\) - distribution table with \(df = 6\) and the right - tail area of \(0.005\).

Answer:

\(3.707\)