Question

find the critical value ( t_{alpha/2} ) needed to construct a confidence interval of the given level with the given sample size. round the answer to at least three decimal places.
level 95\\%, sample size 21.
critical value = \square

Explanation:

Step1: Calculate the significance level $\alpha$

The confidence level is $95\%$, so $\alpha = 1 - 0.95=0.05$. Then $\frac{\alpha}{2}=\frac{0.05}{2}=0.025$.

Step2: Calculate the degrees of freedom $df$

The sample size $n = 21$. The degrees of freedom $df=n - 1=21-1 = 20$.

Step3: Find the critical value from the t - distribution table

Looking up the value in the t - distribution table (or using a statistical software/ calculator) with $df = 20$ and $\frac{\alpha}{2}=0.025$, we get $t_{\frac{\alpha}{2}}=2.086$.

Answer:

$2.086$