# 8.1.1.2 - Minitab Express: Confidence Interval for a Proportion

Before we can construct a confidence interval for a proportion we must first determine if we should use the exact method or the normal approximation method. Recall that if $$np \geq 10$$ and $$n(1-p) \geq 10$$ then the sampling distribution can be approximated by a normal distribution. If this assumption has not been met then the sampling distribution is constructed using a binomial distribution which Minitab Express refers to as the "exact method."

To check this assumption we can construct a frequency table. You first learned how to construct a frequency table in Lesson 2.1.1.2.1 of these online notes. Here is another example:

## MinitabExpress – Frequency Tables

To create a frequency table of dog ownership in Minitab Express:

1. Open the data set:
2. On a PC: In the menu bar select STATISTICS > Describe > Tally
3. On a Mac: In the menu bar select Statistics > Summary Statistics > Tally
4. Double click the variable Dog in the box on the left to insert the variable into the Variable box
5. Under Statistics, check Counts
6. Click OK

This should result in the following frequency table:

Tally
Dog Count
No 252
Yes 272
N= 524
*= 1
Video Walkthrough

Select your operating system below to see a step-by-step guide for this example.

From the frequency table above we can see that there were at least 10 "successes" and at least 10 "failures." In this example a success is defined as answering "yes" to the question "do you own a dog?" A failure is defined as answering "no." Because both $$np \geq 10$$ and $$n(1-p) \geq 10$$, the normal approximation method may be used. In Minitab Express, the exact method is the default method. If there are at least 10 successes and at least 10 failures, then you need to change the method to the normal approximation method.

## MinitabExpress – Confidence Interval for a Proportion (Normal Approximation M

To create a 95% confidence interval of dog ownership using the normal approximation method in Minitab Express:

1. Open the data set:
2. On a PC: In the menu bar select STATISTICS > One Sample > Proportion
3. On a Mac: In the menu bar select Statistics > 1-Sample Inference > Proportion
4. In this case we have our data in the Minitab Express worksheet so we will use the default Sample data in a column
5. Double click the variable Dog in the box on the left to insert the variable into the Sample box
6. Click on the Options tab
7. The default Confidence level is 95
8. Change the Method to Normal approximation because the assumption of $$np \geq 10$$ and $$n(1-p) \geq 10$$ has been met
9. Click OK

This should result in the following output:

 Event: Dog = Yes p: proportion where Dog = Yes Normal approximation is used for this analysis.
Descriptive Statistics
N Event Sample p 95% CI for p
524 272 0.519084 (0.476304, 0.561863)

Video Walkthrough

Select your operating system below to see a step-by-step guide for this example.

## What if the assumption of $$np \geq 10$$ and $$n(1-p) \geq 10$$ is not met? Section

If this assumption is not met then the exact method should be used instead of the normal approximation method. In Minitab Express, this means that in step 8 above the default setting of Exact method should not be changed.

What if we have summarized data and not data in a Minitab Express worksheet?

If you do not have a Minitab Express worksheet filled with data concerning individuals, but instead have summarized data (e.g., the values of $$\widehat{p}$$ and $$n$$), you would skip step 1 above and in step 3 you would select Summarized data. For Number of events enter the number of successes (i.e., $$np$$) and for Number of trials enter the total sample size (i.e., $$n$$).