Which test is parametric for comparing a single sample mean to a known value?

Which test is parametric for comparing a single sample mean to a known value?

• A. Simple t-test
• B. Wilcoxon
• C. Paired samples t-test
• D. One-factorial ANOVA

Answer: (A)

The test that fits a single sample mean against a fixed value using a parametric approach is the one-sample t-test. It directly tests whether the observed mean from your sample differs from the known value (μ0). The calculation centers on t = (M − μ0) / (s/√n), where M is the sample mean, s is the sample standard deviation, and n is the sample size; the test uses the t distribution with n−1 degrees of freedom. This method relies on parametric assumptions, primarily that the data are interval/ratio and approximately normally distributed, which makes it powerful for small samples when those conditions hold. The Wilcoxon test is nonparametric and compares medians rather than means, so it’s used when normality can’t be assumed. The paired samples t-test handles two related or matched samples (before/after, or paired observations), not a single sample against a fixed value. One-factorial ANOVA compares means across three or more independent groups, not a single sample mean to a known value.

The test that fits a single sample mean against a fixed value using a parametric approach is the one-sample t-test. It directly tests whether the observed mean from your sample differs from the known value (μ0). The calculation centers on t = (M − μ0) / (s/√n), where M is the sample mean, s is the sample standard deviation, and n is the sample size; the test uses the t distribution with n−1 degrees of freedom. This method relies on parametric assumptions, primarily that the data are interval/ratio and approximately normally distributed, which makes it powerful for small samples when those conditions hold.

The Wilcoxon test is nonparametric and compares medians rather than means, so it’s used when normality can’t be assumed. The paired samples t-test handles two related or matched samples (before/after, or paired observations), not a single sample against a fixed value. One-factorial ANOVA compares means across three or more independent groups, not a single sample mean to a known value.