﻿ Three Ways to Write a Confidence Interval - MathBootCamps

## Three Ways to Write a Confidence Interval

Assuming that you are familiar with how to calculate a confidence interval as well as how to interpret a confidence interval, you may be curious as to actually write down a final “answer” or result.

Let’s use an example of a confidence interval problem and then see how many ways we can write the final answer.

A college student wishes to estimate the percentage of students on his campus who can name the current president of the college. He chooses a random sample of 347 students and finds that 86 of them can in fact, name the current college president. Help the student estimate the percentage of all students who can name the current president by calculating a 95% confidence interval.

The final answer for this if using the formula is: $0.248 \pm 0.045$.

Note: If you have no idea where that answer comes from, please see the article: calculating a confidence interval for the population proportion.

## Method 1 – Point Estimate +/- Margin of Error

All confidence intervals are of the form “point estimate” plus/minus the “margin of error”. If you are finding a confidence interval by hand using a formula (like I did above), your interval is in this form before you do your addition and subtraction. This is a common way to actually present your confidence interval.

Final Answer: $0.248 \pm 0.045$.

Since this confidence interval is estimating a percentage, it might also be written as:

Final Answer: $24.8\% \pm 4.5\%$.

This would be the method probably used on a news cast or report to a general audience. The student could say “about 24.8% of students at my college can name the college president.” he would then somewhere in his report note that his estimate has a margin of error of 4.5%. If you pay attention to newscasts, they typically show this number on the screen while discussing similar polls.

## Method 2 – As an Interval

If you actually do the two calculations, 0.248 – 0.045 = 0.203 and 0.248 + 0.045 = 0.293, you will get two endpoints. These can be used to write the final answer as well.

Final Answer: (0.203, 0.293) (or equivalently (20.3%, 29.3%) after converting to percentages)

This is typically how a confidence interval will look if you calculating it using technology such as a ti83 or ti84. It’s a little more “mathy” so you might not see it as often in reports to general audiences.

## Method 3 – As an Inequality

Finally, some textbooks (I haven’t seen it ANYWHERE else) like to take the method and help you remember that somewhere in that interval is your population value you are trying to estimate. In this case, you are estimating the population proportion p, so you would write.

Final Answer: 0.203 < p < 0.293 Note that if you were estimating the mean, you would place μ within the inequality.

## Important

If you are taking a statistics course, it is of course important to pay attention to how your professor or textbook prefers to present confidence intervals and generally stick to that method. If you are using confidence intervals in your research, it is probably important to consider your audience. Most people have no trouble understanding the idea of adding and subtracting a margin of error, even if they haven’t had much formal training in statistics. This should be a consideration when you present your findings.

Finally, and most importantly, do take a moment to read about how to interpret confidence intervals. It is easy to get caught up in the math side but you still must know how this applies to real life situations.

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