If the $U$ test is applied in a test whose alternative hypothesis is $\mu_{1} \neq \mu_{2}$ with $n_{1}=7, n_{2}=7, \alpha=0.05$, the null hypothesis can be rejected if
A) $W_{1} \geq 70$ and $W_{2} \geq 70$.
B) $\mathrm{U} \leq 8$.
C) $\mathrm{U}8$.
D) $\mathrm{W}_{1} \leq 70$ or $\mathrm{W}_{2} \leq 70$.

Question

If the $U$ test is applied in a test whose alternative hypothesis is $\mu_{1} \neq \mu_{2}$ with $n_{1}=7, n_{2}=7, \alpha=0.05$, the null hypothesis can be rejected if
A) $W_{1} \geq 70$ and $W_{2} \geq 70$.
B) $\mathrm{U} \leq 8$.
C) $\mathrm{U}>8$.
D) $\mathrm{W}_{1} \leq 70$ or $\mathrm{W}_{2} \leq 70$.

Quizplus · Accepted Answer

The Mann-Whitney U test, often referred to as the U test, is used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed. The critical value of U for rejecting the null hypothesis depends on the sample sizes of the two groups and the significance level ($\alpha$). Given $n_{1} = n_{2} = 7$ and $\alpha = 0.05$, the critical value of U can be looked up in a table specific to the Mann-Whitney U test. For these sample sizes and a two-tailed test (since the alternative hypothesis is $\mu_{1} \neq \mu_{2}$), the critical value of U to reject the null hypothesis is indeed less than or equal to 8. This means if the calculated U statistic is 8 or less, the null hypothesis can be rejected, indicating a significant difference between the two groups.

If The UUU Test Is Applied in a Test Whose Alternative Hypothesis Is

If The $U$ Test Is Applied in a Test Whose Alternative Hypothesis Is