How do you Calculate a One Sample T Test?

One sample t-test is used to match the mean of single sample data to a known or hypothetical population mean. The one sample t-test is a constant quantity test. This test is also known as a single sample t-test. Where t is the variable.

Common use of one sample t-test

One sample t-test is generally used to test the following-

  • Statistical difference between a variable score and a zero.
  • Statistical value from a mean value to a known or hypothesized value of the mean in the population.

Single sample t-test will compare only a single sample mean to a specified constant instead of comparing sample mean between two or more groups.

Data Requirement for one sample t-test

To calculate the single t-test your data must meet following requirements:

  • A continuous test variable (t)
  • Independent scores of test variables.
  • Random sample of population data
  • Normal distribution of the sample and population on the test value
  • Homogeneity of variances.
  • No outliers

One sample t-test example

Let’s take an example from your business sales department.

Question: You want to improve a sales performance report. In the past years your sales were $100 per transaction. This year after training, your sales data indicates mean sales of $130 with a sample of twenty five sales persons with a standard deviation of $15. Did the training give any result to you? Test the hypothesis at a 5% alpha level.


Step 1:

Null hypothesis value: where there is no increase in sales

H0: μ = $100.

Step 2:

Alternate hypothesis: where there is increase in sales

H1: μ > $100.

Step 3:

According to question:

  • The sample mean(x̄). This is often given within the question as $130.
  • The population mean(μ). Given as $100 (from past data).
  • The sample standard deviation(s) = $15.
  • Number of observations(n) = 25.

Step 4:

t-score formula says:

t = (130 – 100) / ((15 / √(25))

t = (30 / 3) = 10

This is your calculated t-value.

Step 5:

Find T-table values.

To find t-table value we need two variables:

  • Alpha value i.e 5% given in the questions above
  • Degrees of freedom i.e. number of items in the sample minus 1


According to the above distribution table; the intersection of degrees of freedom and alpha is 1.711.


There is a significant difference between our hypothesis t-value and distribution t-table value does not fall in the range calculated above in step 4 and step 5. So we will reject the null hypothesis. This means your sales training got success as its value is greater.

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