Watch the video or read the steps below:
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 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 5: Divide your std dev (step 1) by the square root of your sample size.
18.172 / √(10) = 5.75
Step 6: : Multiply step 4 by step 5.
2.821 × 5.75 = 16.22075
Step 7: For the lower end of the range, subtract step 6 from the mean (Step 1).
71 – 16.22075 = 54.77925
Step 8: For the upper end of the range, add step 6 to the mean (Step 1).
71 + 16.22075 = 87.22075
That’s how to construct a confidence interval using the t-distribution!
Watch the video or read the article below:
Sample problem: Construct a 95 % confidence interval an experiment that found the sample mean temperature for a certain city in in August was 101.82, with a population standard deviation of 1.2. There were 6 samples in this experiment.
Step 1: Subtract the confidence level (Given as 95 percent in the question) from 1 and then divide the result by two. This is your alpha level, which represents the area in one tail.
(1 – .95) / 2 = .025
Step 2: Subtract your result from Step 1 from 1 and then look that area up in the middle of the z-table to get the z-score:
- 1 – 0.25 = 0.975
- z score = 1.96.
Step 3: Plug the numbers into the second part of the formula and solve:
z* σ / (√n)
= 1.96 * 1.2/√(6)
= 1.96 * 0.49
Step 4: For the lower end of the range, subtract step 3 from the mean.
101.82 – 0.96 = 100.86
Step 5: For the upper end of the range, add step 3 to the mean.
101.82 + 0.96 = 102.78.
The CI is (100.86,102.78)
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