How to apply the one sample t-test

By Ron Pereira Updated on May 18th, 2026

Last night we discussed the history and background of the one sample t-test. As promised, tonight we will discuss how it is you actually use the slick little hypothesis test. At the end of this post is a free case study available for download.

When to use it

We may use the one-sample t-test to compare a sample mean to a target value when we don’t know the true population standard deviation (s). Also, as we discussed last night, the one-sample t-test allows us to work with smaller sample sizes.

Assumptions

There are a few assumptions we need to consider prior to running the one-sample t-test.

Our data should be stable and not trending. If, for example, our data has been trending up for the last 3 months, the one-sample t-test should not be employed. How to check this? Throw the data into a control chart and see what it tells you.
The data should be normally distributed. There are fancy statistical tests, such as the Anderson-Darling test, that can help us here. I always recommend people first study the “shape” of the data in a simple histogram. If the shape looks normal to the eye, I say press on with the one-sample t-test.

State the null and alternate hypothesis

If we satisfy the assumptions, it is now time to state the null (Ho) and alternative (Ha) hypotheses. For the standard one-sample t-test, it will look like this, assuming our “target” value is 25 for this example.

Ho: mu = 25
Ha: mu not = 25

Determine the level of risk you are willing to take

With hypothesis testing, we never accept anything. Instead, we either reject or fail to reject a hypothesis, just like the American judicial system, where we never prove someone innocent. Instead, they are either guilty or not guilty beyond a reasonable doubt.

So, with hypothesis testing, we need to state the level of risk, or reasonable doubt, we are willing to take. In most cases, an “alpha risk,” as it is called, of 5% is commonly chosen.

Run the test and make a decision

Now then, we have met our assumptions and stated the level of risk we are willing to take. Now all that’s left is to run the test and make a, gulp, decision.

When we run the test we will get a P value which is the is the probability of incorrectly rejecting the null hypothesis. Just remember this saying, “if P is low, Ho must go.”

So, we run the test and examine the P value. If the P value is less than 5% we reject Ho and state that the alternate hypothesis is true at the confidence level of 100*(1-P value)%. If it is greater than 5% we fail to reject the null hypothesis.

We will also get information on confidence intervals which basically tells us a range of where we may expect to see our data.

Ron Pereira

Ron has more than 20 years of experience in various manufacturing, supply chain, and senior leadership roles. Ron has held the titles of process engineer, engineering manager, master black belt, and director of manufacturing & continuous improvement. In 2002 Ron was the first American to win the Nokia Global Six Sigma and Overall Quality award in Helsinki, Finland. Ron holds a bachelor's degree in automated manufacturing and an MBA in technology management.

marimuthu
April 16, 2008 - 5:35 am
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i have got thosound samples in excel sheet how to import the data into spss i dont know,this is questionar type ,how to select variable how to measure