# 1-Sample t

## Summary

Analyzes the difference between an observed process mean and a specified value.

• Is the mean of the process significantly different from a specified value such as a previously known value of the process mean or a nominal specification?
When to Use Purpose
Pre-project Verify the process is producing output significantly different from expectations, which validates the need for an improvement project.
Mid-project Test whether the output changes significantly when an input is controlled at a new setting or a previously uncontrolled setting is now controlled.
Mid-project Verify changes from the pre-project standard throughout the course of making improvements.
End of project Verify the mean output from the controlled improved process is different from the pre-project mean. Of course, this step assumes that one of the goals of the project was to shift the process mean.

### Data

Continuous Y (output)

## How-To

1. Verify the measurement system for the Y data is adequate.
2. Develop a data collection strategy. For example, determine who should collect the data, where and when the data should be collected, how many data values are needed, the preciseness of the data, how to record the data, and so on.
3. Collect process data, and enter the values into a single column in a Minitab worksheet.
4. Enter the standard or benchmark to compare the process data against.
5. Determine your hypothesis. You are trying to prove the alternative hypothesis (Ha) with the data. In a 1-sample t-test, the alternative hypothesis states that the process mean is greater than, less than, or not equal to a benchmark value. The null hypothesis (Ho) is the opposite of the alternative hypothesis.
6. You can also perform the test without the raw data if you know the mean, standard deviation, and sample size.

## Guidelines

• Develop a sound data collection strategy to ensure your conclusions are based on truly representative data.
• Use Minitab’s Power and Sample Size command to determine the sample size necessary to detect the smallest difference of interest with sufficient power.
• The data must be continuous and reasonably normal. The 1-sample t-test is very robust to violations of the normality assumption, especially if the sample size is large (n > 25).
• It is good practice to graph your data when you use a statistical test. For the 1-sample t-test, use normal probability plots to evaluate normality and histograms to identify outliers.
• If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.
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