Test of significance for comparing means of 2 group is
**Core Concept**
The question is testing the understanding of statistical hypothesis testing, specifically for comparing means between two groups. This involves selecting the appropriate statistical test to determine if there is a significant difference between the means of two independent or paired samples.
**Why the Correct Answer is Right**
The correct test for comparing means of two groups depends on the type of data (parametric or non-parametric) and the level of measurement (continuous or categorical). For comparing means of two independent groups with normally distributed data, the most commonly used test is the **t-test**, also known as the Student's t-test. This test calculates the t-statistic, which is a ratio of the difference between the means and the standard error of the difference, and then determines the p-value, which indicates the probability of observing the t-statistic under the null hypothesis of no difference between the means.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the Wilcoxon rank-sum test (also known as the Mann-Whitney U test) is used for non-parametric data, which does not meet the assumption of normality required for the t-test.
**Option B:** This option is incorrect because the one-way ANOVA (Analysis of Variance) is used for comparing means of three or more groups, not two groups.
**Option C:** This option is incorrect because the paired t-test is used for comparing means of two related groups, not independent groups.
**Clinical Pearl / High-Yield Fact**
When selecting a statistical test for comparing means, always check the assumptions of normality and equal variances before choosing between the t-test and Wilcoxon rank-sum test.
**Correct Answer: D. t-test**