How to Find a Confidence Interval: Overview
When we talk about confidence intervals, we’re dealing with data. For example, let’s say the manager for that job you applied for told you he would get back with you in a “couple of days.” A couple of days could mean two. Or three. Or there might be a paperwork backlog and it could be a week. It definitely doesn’t mean in an hour. So your confidence interval would probably be between 2 and 4 days.
Perhaps the trickiest part of confidence intervals is recognizing the various parts needed for the formula, like z a/2. This article breaks everything down into simple steps and shows you how to find the most common confidence intervals for population proportions.
If you want to find the confidence interval for a sample, click here.
How to Find a Confidence Interval for a Proportion
Sample question: 510 people applied to the Bachelor’s in Elementary Education program at Florida State College. Of those applicants, 57 were men. Find the 90% confidence interval of the true proportion of men who applied to the program.
Step 1: Read the question carefully and figure out the following variables:
- α : subtract the given confidence interval from 1.
- z α/2: divide α by 2, then look up that area in the z-table. Not sure how to read a z table? See this article, area to the right of a z-score for an explanation on how to read the z-table.
.1/2=.0500. The closest z-value to an area of .0500 is 0.13
- : Divide the proportion given (i.e. the smaller number)by the sample size.
- : Subtract from 1.
1-0.112 = 0.888
Step 2: Multiply by .
0.112 x 0.888 = 0.099456
Step 3: Divide step 2 by the sample size.
0.099456 / 510 = 0.000195011765
Step 4:Take the square root of step 3:
sqrt(0.000195011765) = 0.0139646613
Step 5: Multiply step 4 by z a/2:
0.0139646613 x 0.13 = 0.0182
Step 6:: For the lower percentage, subtract step 5 from .
0.112-0.0182 = 0.0938 = 9.38%
Step 7:For the upper percentage, add step 5 to .
0.112 + 0.0182 = 0.1302 = 13.02%
That’s how to find a confidence interval!
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