Calculating Confidence Intervals for Proportions in Minitab

A common question I get asked is: how accurate are my defect rate predictions?

If you are inspecting a sample of items, and there are some defects or errors, you can easily calculate the defect rate by taking the number of defects divided by the number of samples. But what if you want to calculate a confidence interval to understand how good or bad it is within the population?

Let’s say we are reviewing applications for a job opening at a nonprofit, and you want to inspect the applications to see which ones are actually coming from “local” candidates (within 20 miles of the facility, which was part of your requirements).

If you have 107 applications, but don’t have time to check all of them individually, you could take a sample of them (n=33) and perform analysis on the sample to predict the results of all 107 applications. This example is common in manufacturing, except you might be inspecting parts in a large shipment, to see if the shipment should be accepted.

You discover that 4 applications out of the 33 inspected were not from the 20-mile radius requirement. That comes out to 4/33 = 12.1%.

How many applications in the population of 107 are likely to be from outside the area? Based on our small sample, you would guess about 12%, or 13 applications. But what kind of range in results should we expect? 11-13? 10-14? 8-16?

A confidence interval for the true percentage is needed to answer that question, but how do you use Minitab to calculate this?

There isn’t a section called Confidence Intervals in Minitab 18. Intervals are often embedded into other analysis.

Since percentages are often called proportions, we look in the menu under Stat –> Basic Statistics –> 1 Proportion…

Next, select “Summarized data” from the dropdown

This section is technically the hypothesis test area, but it will also generate a confidence interval.

Plugging in the results above to the Minitab window, we get the following results

```Descriptive Statistics
N Event     Sample p    95% CI for p
33     4     0.121212    (0.034033, 0.282016)```

The confidence interval (CI) for the proportion (p) is between 0.034 and 0.282, which equates to 3.4% and 28.2%

Therefore, there is a 95% chance that the true proportion of applications outside the local area is between 3 and 30 out of the 107 total applications. That’s a wide range of results!

Even though we only sampled 33 applications, it does give us some information about the true percentage. If you want a more accurate prediction, you will need to review more samples.

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