Question

Which test is most appropriate for testing the significance of the difference between two small sample means?

• A. Z-test
• B. t-test
• C. Chi-square test
• D. F-test

Hint:

Use the \textbf{t-test} when:

• Sample size is small (\(n<30\))
• Population variance is unknown

It is commonly used to test the significance of the difference between two sample means.

Answer 1

The Correct Option is B

Concept:
When comparing the means of two samples, the choice of test depends mainly on the sample size and knowledge of population variance.

• If the sample size is large (\(n \ge 30\)), the Z-test is generally used.
• If the sample size is small (\(n<30\)) and the population variance is unknown, the Student's t-test is used.

The t-test is specifically designed for small samples and accounts for additional uncertainty in estimating the population variance.
Step 1: Identify the condition given in the question.
The problem states that the samples are small.
Step 2: Choose the appropriate statistical test.
For small sample means, the correct test is the Student's t-test.
Step 3: State the conclusion.
\[ \therefore \text{The appropriate test for comparing two small sample means is the t-test.
\]