Question

use the t distribution table to find the $t_{\alpha / 2}$ value for a $95 \\%$ confidence interval for the mean when the sample size is 37.
$t_{\alpha / 2}=\square$

Explanation:

Step1: Calculate degrees of freedom

Degrees of freedom \( df=n - 1\). Given \(n = 37\), so \(df=37-1 = 36\)

Step2: Determine \(\alpha\) value

For a \(95\%\) confidence interval, \(\alpha=1 - 0.95=0.05\). Then \(\frac{\alpha}{2}=\frac{0.05}{2}=0.025\)

Step3: Look up in t - distribution table

Using the t - distribution table (or a t - distribution calculator), with \(df = 36\) and \(\frac{\alpha}{2}=0.025\), the \(t_{\alpha/2}\) value is approximately \(2.028\)

Answer:

\(2.028\)