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.
Null hypothesis value: where there is no increase in sales
H0: μ = $100.
Alternate hypothesis: where there is increase in sales
H1: μ > $100.
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.
t-score formula says:
t = (130 – 100) / ((15 / √(25))
t = (30 / 3) = 10
This is your calculated t-value.
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.