About test of significance between two large population, one of the following statements is true –
**Core Concept:** Test of significance is a statistical method used to determine if a difference between two groups is due to chance or real.
**Why the Correct Answer is Right:** The correct answer is D, the two-tailed test. A two-tailed test is used when we are interested in the direction of the difference between two populations. For example, if we are comparing the mean heights of two groups, we would want to know if one group is taller or shorter than the other. In this case, we would perform a two-tailed test, as we are interested in both the absolute difference (taller or shorter) and the relative difference (the degree of difference).
**Why Each Wrong Option is Incorrect:**
A. One-tailed test (Option A) is used when we are only interested in the direction of the difference between populations. For example, comparing mean heights of two groups, we would only be interested in whether one group is taller. In this case, we would use a one-tailed test.
B. A two-tailed test (Option B) is used when we are interested in both the absolute and relative differences between populations. As stated before, we would use a two-tailed test when comparing mean heights of two groups, as we are interested in both the absolute (taller or shorter) and relative (degree of difference) differences.
C. A one-tailed test (Option C) is used when we are only interested in the absolute difference between populations. For example, comparing mean heights, we would only be interested in whether one group is taller or shorter, not the degree of difference.
**Clinical Pearl / High-Yield Fact:** When deciding whether to use a one-tailed or two-tailed test, consider the research question being asked. If the research question focuses on the direction of the difference, select a one-tailed test. If the research question considers both the direction and degree of difference, select a two-tailed test.
**Correct Answer:** D. Two-tailed test