Question

1) Find the critical value for a 95% confidence interval when the sample size is 30.

Answer 1

To help you find critical values for the t-distribution, you can use the last row of the t-table, which lists common confidence levels, such as 80%, 90%, and 95%. To find a critical value, look up your confidence level in the bottom row of the table; this tells you which column of the t-table you need. Intersect this column with the row for your df (degrees of freedom). The number you see is the critical value (or the $t_{\alpha /2}$ - value) for your confidence interval.

Given

Confidence level = 95%

Sample size (n) = 30

So,

Degrees of freedom (d.f) = n -1 = 30 -1 =29

Go to the bottom of the table, find the column for 95%, and intersect it with the row for df = 29.

This gives you a $t_{\alpha /2}$ value of 2.045.

So, the critical value for a 95% confidence interval when the sample size is 30 is 2.045