Question

using the t distribution table, find the critical value(s) for the t test for a two - tailed test with ( n = 13 ) and ( alpha = 0.10 ). enter the answers separated by a comma if needed. critical value( (s)=)

Explanation:

Step1: Calculate degrees of freedom

Degrees of freedom \(df=n - 1\). Given \(n = 13\), so \(df=13 - 1=12\).

Step2: Determine critical value for two - tailed test

For a two - tailed test with \(\alpha=0.10\), the significance level in each tail is \(\frac{\alpha}{2}=\frac{0.10}{2}=0.05\).
Looking up the \(t\) - distribution table with \(df = 12\) and \(\alpha/2=0.05\), we get the critical value \(t_{\alpha/2,df}=t_{0.05,12}=1.782\).
Since it is a two - tailed test, the critical values are \(\pm t_{\alpha/2,df}\), so the critical values are \(\pm1.782\).

Answer:

\(\pm 1.782\)