# How do you Calculate a One Sample T Test?

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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

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.

Solution:

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

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

t:25-1=24 According to the above distribution table; the intersection of degrees of freedom and alpha is 1.711.

## Conclusion

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.