**Core Concept**
The comparison of mean values between two independent groups is a fundamental problem in statistical analysis. In this scenario, we are dealing with a paired or independent samples t-test, which is used to determine if there is a significant difference between the means of two groups.

**Why the Correct Answer is Right**
The independent samples t-test is the appropriate test of significance because it allows us to compare the means of two independent groups, each with a sample size of 50. This test is based on the assumption that the population variances are equal (homoscedasticity) and that the data follows a normal distribution. The test statistic is calculated as the difference between the means of the two groups divided by the standard error, which is a measure of the variability between the groups.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the paired t-test is used to compare two related samples, not independent groups.
**Option B:** This option is incorrect because the Analysis of Variance (ANOVA) is used to compare more than two independent groups, not two groups.
**Option C:** This option is incorrect because the Wilcoxon rank-sum test is a non-parametric test used to compare two independent groups, but it is not as sensitive as the independent samples t-test.

**Clinical Pearl / High-Yield Fact**
When comparing means between two independent groups, always check for homoscedasticity (equal variances) and normal distribution of the data before selecting the appropriate test of significance.

**Correct Answer: C.