Question

The test of significance of differences between two means in small samples is calculated by:

• A. \(\chi^2\) (chi-square) test
• B. Z-test
• C. t-test
• D. F-test

Hint:

Statistical tests:
- t-test: Small samples (n < 30).
- Z-test: Large samples (n > 30).
- Chi-square: Categorical data.
- F-test: Comparing variances.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question tests knowledge of statistical tests for comparing means.

Step 2: Detailed Explanation:
The t-test is used to test the significance of differences between two means when the sample size is small (n < 30).
It was developed by W.S. Gosset (Student's t-test).
Chi-square test (A): Used for categorical data.
Z-test (B): Used for large samples (n > 30).
F-test (D): Used for comparing variances.
Thus, the t-test is used for small samples.

Step 3: Final Answer:
Thus, the t-test is used for small samples, which corresponds to option (C).
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