The dependent t-test (also known as the paired t-test or paired-samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference between these two means.

We use the paired t-test if we have two measurements on the same item, person or thing. We should also use this test if we have two items that are being measured with a unique condition.

For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.

In this case, Kristen assesses the students' knowledge of French vocabulary at the start of the semester and then again at the end of the semester.

So, she collects data before and after the semester for vocabulary learning in introductory-level French class.

Thus, she is using a paired t-test to analyze whether the French students significantly increased their knowledge of French vocabulary.

The hypothesis is defined as:

H₀: There is no difference between the two means, i.e. μ₁ - μ₂ = 0.

Hₐ: There is a significant difference between the two means, i.e. μ₁ - μ₂ ≠ 0.

The test statistic is:

t = Sample mean difference ÷ (Standard deviation of difference/ Sample size)

Thus, Kristen should use the paired t-test.

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