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

Step 1: Understanding the Question
The question asks to identify the correct statistical test for comparing the means of two groups when the sample sizes are small.
Step 2: Detailed Explanation
Let's analyze the purpose of each test listed:

Z-test: This test is used to compare means when the sample sizes are large (typically \(n>30\)) or when the population variances are known. The large sample size allows us to rely on the Central Limit Theorem.

t-test (Student's t-test): This test is specifically designed for situations where the sample sizes are small (typically \(n<30\)) and the population variances are unknown. It is the standard method for comparing the means of two small samples.

Chi-square (\(\chi^2\)) test: This test is used for analyzing categorical data. It is used for goodness-of-fit tests or tests of independence between two categorical variables, not for comparing means.

F-test: This test is primarily used to compare the variances of two populations. It is also the underlying test in Analysis of Variance (ANOVA), which compares the means of three or more groups.

The key phrase in the question is "two small sample means." This directly points to the t-test as the most appropriate choice.
Step 3: Final Answer
The most appropriate test for testing the significance of the difference between two small sample means is the t-test.