Question

find the critical value $t_{c}$ for the confidence level $c = 0.95$ and sample size $n = 27$. click the icon to view the t - distribution table. $t_{c}=\square$ (round to the nearest thousandth as needed.)

Explanation:

Step1: Calculate degrees of freedom

Degrees of freedom \(df=n - 1\). Given \(n = 27\), so \(df=27-1 = 26\).

Step2: Determine the significance level

Confidence level \(c = 0.95\), significance level \(\alpha=1 - c=1 - 0.95 = 0.05\). For a two - tailed test, \(\frac{\alpha}{2}=\frac{0.05}{2}=0.025\).

Step3: Look up the value in the t - distribution table

Using the t - distribution table with \(df = 26\) and \(\frac{\alpha}{2}=0.025\), we find the critical value.

Answer:

\(t_{c}=2.056\)