Which test is commonly used when the sample variance is unknown and the sample size is small?

• A. T-test.
• B. Z-test.
• C. Chi-square test.
• D. ANOVA.

Answer: (A)

When you don’t know the population variance and you have a small sample, use the t-test. The reason is that you must estimate the population standard deviation from the sample, which adds extra uncertainty. The t-test uses this estimate and the t distribution, which has heavier tails to reflect that uncertainty. The result is more conservative, with wider confidence intervals and larger critical values when the sample is small. As the sample gets larger, the t distribution closely approximates the normal distribution, which is why a z-test is appropriate only when the variance is known or the sample is large. Other tests fit different situations: the z-test relies on known variance or large samples; the chi-square test is for categorical data or to test variances; ANOVA compares means across multiple groups.