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Confidence Interval For a Sample: Overview
When you don’t know anything about a population’s behavior (i.e. you’re just looking at data for a sample), you need to use the t-distribution to find the confidence interval. That’s the vast majority of cases: you usually don’t know population parameters, otherwise you wouldn’t be looking at statistics!
The confidence interval tells you how confident you are in your results. With any survey or experiment, you’re never 100% sure that your results could be repeated. If you’re 95% sure, or 98% sure, that’s usually considered “good enough” in statistics. That percentage of sureness is the confidence interval.
Confidence Interval For a Sample: Steps
A group of 10 foot surgery patients had a mean weight of 240 pounds. The sample standard deviation was 25 pounds. Find a confidence interval for a sample for the true mean weight of all foot surgery patients. Find a 95% CI.
Step 2: Subtract the confidence level from 1, then divide by two.
(1 – .95) / 2 = .025
Step 3: Look up your answers to step 1 and 2 in the t-distribution table. For 9 degrees of freedom (df) and α = 0.025, my result is 2.262.
|df||α = 0.1||0.05||0.025||0.01||0.005||0.001||0.0005|
Step 4: Divide your sample standard deviation by the square root of your sample size.
25 / √(10) = 7.90569415
Step 5: Multiply step 3 by step 4.
2.262 × 7.90569415 = 17.8826802
Step 6: For the lower end of the range, subtract step 5 from the sample mean.
240 – 17.8826802 = 222.117
Step 7: For the upper end of the range, add step 5 to the sample mean.
240 + 17.8826802 = 257.883
That’s how to find the confidence interval for a sample!
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