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The t-Test in Statistics

The t-test is a statistical test used to determine whether there is a significant difference between the means of two groups. It is based on the t-distribution and is commonly employed when the sample size is small or the population standard deviation is unknown.

Types of t-Tests:

• One-Sample t-Test: Compares the mean of a sample to a known or assumed population mean.
• Paired Samples t-Test: Compares the means of two related samples, such as before and after an intervention.
• Independent Samples t-Test: Compares the means of two independent samples.

Situations where the t-Test is Applied:

• Comparison of average values between two groups, such as the average test scores of two classes.
• Investigation of changes before and after an intervention or treatment.
• Testing whether a sample comes from a population with a known mean.

Example:

Suppose we have two groups of students, and we want to know if there is a significant difference in their average test scores. An independent samples t-test could be used to perform this comparison.