Recently, a legislative committee commissioned a study of incomes in a western state. At issue was whether the ratings of the legislature's performance differed between rural citizens and city residents. A random sample of 25 city residents and 35 rural residents was asked to rate the performance of the legislature on a scale of 1 to 100. The analysts believe that the population distribution of ratings would be highly skewed so they decided to use the Mann-Whiney U test to test whether there is a difference in median ratings by the two groups. Given this information, which of the following is the correct critical value if the test is to be conducted at the .10 level of significance?
A) z = 1.96
B) t = 2.0357
C) U = 437.5
D) z = 1.645

Question

Quizplus · Accepted Answer

The Mann-Whitney U test is a non-parametric test used to compare two independent samples. It is appropriate when the assumptions for the t-test are not met, such as when the data are not normally distributed. Since the test is non-parametric, it does not rely on the normal distribution, and the critical values are based on the normal approximation for large samples. At the .10 level of significance (10% significance level), the critical value for a two-tailed test from the standard normal distribution is z = 1.645.

Recently, a Legislative Committee Commissioned a Study of Incomes in a Western