Answer:
Confidence levels are expressed as a percentage (for example, a 95% confidence level). It means that should you repeat an experiment or survey over and over again, 95 percent of the time your results will match the results you get from a population (in other words, your statistics would be sound!). Confidence intervals are your results…usually numbers. For example, you survey a group of pet owners to see how many cans of dog food they purchase a year. You test your statistics at the 99 percent confidence level and get a confidence interval of (200,300). That means you think they buy between 200 and 300 cans a year. You’re super confident (99% is a very high level!) that your results are sound, statistically.
Confidence Interval For a Sample: Steps
Question:
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 1: Subtract 1 from your sample size. 10 – 1 = 9. This gives you degrees of freedom, which you’ll need in step 3.
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.
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, hope that helped!
