# 8.2.2.2 - Minitab: Confidence Interval of a Mean

8.2.2.2 - Minitab: Confidence Interval of a Mean

Here you will learn how to use Minitab to construct a confidence interval for a mean. The procedure is similar to the one that you learned earlier in this lesson for constructing a confidence interval for a proportion. The following example walks through this procedure when data are in a Minitab work. At the bottom of this page you will find instructions for using Minitab with summarized data.

## Minitab® – Confidence Interval for a Mean

To create a 95% confidence interval of mean height in Minitab:

1. Open the data set: fall2016stdata.mpx
2. In Minitab, select Stat > Basic Statistics > 1-sample t
3. In this case we have our data in the Minitab worksheet so we will use the default One or more samples, each in a column
4. Double click the variable Height in the box on the left to insert the variable into the box
5. Select Options
6. The default Confidence level is 95
7. Click OK and OK

This should result in the following output:

#### Descriptive Statistics

N Mean StDev SE Mean 95% CI for $$\mu$$
525 67.009 4.462 0.195 (66.627, 67.392)

$$\mu$$: mean of Height

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

If you do not have a Minitab worksheet filled with data concerning individuals, but instead have summarized data (e.g., the values of $$s$$, $$\overline{x}$$, and $$n$$), you would skip step 1 above and in step 3 you would select Summarized data

# 8.2.2.2.1 - Example: Age of Pitchers (Summarized Data)

8.2.2.2.1 - Example: Age of Pitchers (Summarized Data)

## Example: Estimating the average MLB Pitcher's age

In a sample of 30 current MLB pitchers, the mean age was 28 years with a standard deviation of 4.4 years. Construct a 95% confidence interval to estimate the mean age of all current MLB pitchers.

We know that n = 30, $$\bar{x}=28$$, and s = 4.4.

To create a 95% confidence interval of mean age in Minitab:

1. In Minitab, select Stat > Basic Statistics > 1-sample t
2. In this case we have summarized data so select Summarized Data from the dropdown
3. Enter 30 for the sample size, 28 for the sample mean and 4.4 for the standard deviation.
4. Select Options
5. The default Confidence level is 95
6. Click OK and OK

This should result in the following output:

#### Descriptive Statistics

N Mean StDev SE Mean 95% CI for $$\mu$$
30 28.000 4.400 0.803 (26.357, 29.643)

$$\mu$$: population mean of sample

We are 95% confident that the population mean age is between 26.357 and 29.643 years.

# 8.2.2.2.2 - Example: Coffee Sales (Data in Column)

8.2.2.2.2 - Example: Coffee Sales (Data in Column)

For 48 days data concerning sales were collected from one student-run cafe. Let's construct a 95% confidence interval for the mean number of coffees sold per day.

To create a 95% confidence interval of mean number of coffees sold per day in Minitab:

1. Open the file: cafedata.mpx
2. In Minitab, select Stat > Basic Statistics > 1-sample t
3. In this case the data is in a worksheet so select use One or more samples, each in a column
4. Select the variable Coffees
5. Select Options
6. The default Confidence level is 95
7. Click OK and OK

This should result in the following output:

#### Descriptive Statistics

N Mean StDev SE Mean 95% CI for $$\mu$$
47 21.51 11.08 1.62 (18.26, 24.76)

$$\mu$$: population mean of Coffees

We are 95% confident that the population mean number of coffees solder per day is between 18.26 and 24.76.

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