Assume you want to construct a 90% confidence interval from sample of a normally distributed population. The sample size is 37. Find the critical value ta/2.

Question

I'm not exactly sure how to solve this, could someone explain?

Answer 1

The above is an extract from a t test table. The last column contains figures for a 2-tailed 90% confidence interval. For this we use ɑ/2=0.05 or 5% being half the difference between 90% and 100%. The distribution curve is symmetrical about the mean so to get the confidence “width” to be 90% of the area beneath the curve, we need 95% of what is above the mean—the right half of the distribution. The first column of the table contains the number of degrees of freedom (dof), which in this case is 37-1=36, one less than the sample size. From the table we see that for dof=30, the critical value is 1.697 and for dof=40 it’s 1.684. If we interpolate linearly between these values we estimate that for dof=36, the value is about 1.689.