Which test is described as a nonparametric test designed to test the null hypothesis with two independent samples from the same population?

Which test is described as a nonparametric test designed to test the null hypothesis with two independent samples from the same population?

• A. ANOVA
• B. Student's T-Test
• C. Mann-Whitney U Test
• D. Chi-square

Answer: (C)

The idea being tested is how to compare two independent samples when you don’t want to assume anything about the distribution of the data. The Mann-Whitney U test is the nonparametric choice for this situation. It asks whether the two samples come from the same population by looking at the ranks of all observations together rather than their actual values. If there’s no real difference, the ranks from both groups are about the same, so neither group tends to have consistently higher values than the other. Because it uses ranks, it doesn’t require normal distribution and works well with ordinal data or small samples. If one group tends to produce larger values, the sum of its ranks will be higher and the test will indicate a difference. This is exactly what the description implies: a nonparametric test designed to test the null hypothesis with two independent samples from the same population. Other tests either assume normality and compare means (like a t-test), extend to more than two groups (like ANOVA), or apply to categorical data (like Chi-square), so they don’t fit the scenario as directly as the Mann-Whitney U test.

The idea being tested is how to compare two independent samples when you don’t want to assume anything about the distribution of the data. The Mann-Whitney U test is the nonparametric choice for this situation. It asks whether the two samples come from the same population by looking at the ranks of all observations together rather than their actual values. If there’s no real difference, the ranks from both groups are about the same, so neither group tends to have consistently higher values than the other.

Because it uses ranks, it doesn’t require normal distribution and works well with ordinal data or small samples. If one group tends to produce larger values, the sum of its ranks will be higher and the test will indicate a difference. This is exactly what the description implies: a nonparametric test designed to test the null hypothesis with two independent samples from the same population.

Other tests either assume normality and compare means (like a t-test), extend to more than two groups (like ANOVA), or apply to categorical data (like Chi-square), so they don’t fit the scenario as directly as the Mann-Whitney U test.