# 8.2.2.2 - Minitab: Confidence Interval of a Mean

8.2.2.2 - Minitab: Confidence Interval of a MeanHere 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:

- Open the data set: fall2016stdata.csv
- In Minitab, select
*Stat > Basic Statistics > 1-sample t* - 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* - Double click the variable
*Height*in the box on the left to insert the variable into the box - Select
*Options* - The default
*Confidence level*is*95* - Click OK and OK

This should result in the following output:

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:

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

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

This should result in the following output:

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.