Construct a Confidence Interval with a t-distribution: Overview
You may be asked in elementary statistics to construct a confidence interval from a given set of data. If you have one small set of data (under 30 items), you’ll want to use the t-distribution instead of the z-distribution to construct your confidence interval. Thanks to the t-distribution table, only a few short steps are needed to calculate the t-distribution.
Construct a Confidence Interval : Steps
Sample problem: Construct a 98% Confidence Interval based on the following data: 45, 55, 67, 45, 68, 79, 98, 87, 84, 82.
Step 2: Subtract 1 from your sample size to find the degrees of freedom (df). We have 10 numbers listed, so our sample size is 10, so our df = 9. You’ll also need this number in step 4.
Step 3: Subtract the confidence level from 1, then divide by two. This is your alpha level.
(1 – .98) / 2 = .01
Step 4: Look up df (Step 2) and α (Step 3) in the t-distribution table. For df = 9 and α = .01, the table gives us 2.821.
Step 4:Divide your std dev (step 1) by the square root of your sample size.
18.172 / √(10) = 5.75
Step 5: : Multiply step 3 by step 4.
2.821 × 5.75 = 16.22075
Step 6: For the lower end of the range, subtract step 5 from the mean (Step 1).
71 – 16.22075 = 54.77925
Step 7: For the upper end of the range, add step 5 to the mean (Step 1).
71 + 16.22075 = 87.22075
That’s how to construct a confidence interval using the t-distribution!
Like the explanation? Check out our statistics how-to book, with a how-to for every elementary statistics problem type.
Questions? Check out our FREE forum. Our resident stats expert (the “Stats Guy”) is on hand to answer your tricky statistics questions.
Check out our Youtube channel for more statistics help and tips.