**Core Concept**
The relationship between the mean heights of two groups of children can be studied using statistical methods to compare the central tendency of the two populations.

**Why the Correct Answer is Right**
To compare the mean heights of two groups, the most appropriate statistical test is the two-sample t-test, also known as the independent samples t-test. This test assesses whether the means of the two groups are significantly different from each other, taking into account the variability within each group. The two-sample t-test is a parametric test, which means it assumes a normal distribution of the data and equal variances between the two groups.

**Why Each Wrong Option is Incorrect**
**Option A:** The Mann-Whitney U test is a non-parametric test used to compare the medians of two independent groups, not the means. It is more robust to outliers and non-normal data but assumes no relationship between the variables.
**Option B:** The ANOVA (Analysis of Variance) test is used to compare the means of three or more groups, not two.
**Option C:** The chi-square test is used for categorical data and is not suitable for comparing means of continuous data like height.

**Clinical Pearl / High-Yield Fact**
When comparing means of two groups, it is essential to check for normality and equal variances before using the two-sample t-test. Failure to do so can lead to incorrect conclusions.

**Correct Answer: D. Two-sample t-test.**