A researcher wants to determine whether the means of two independent populations are the same.She has two independent random samples, one from each population, shown in the following table: $\quad $ $\quad $ $\quad $ $\quad $Sample I $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $Sample II
$\begin{array}{llll|lllll}
\hline 11.5 & 15.7 & 22.8 & 22.5 & 12.6 & 13.8 & 17.5 & 10.7 & 13.5 \
12.4 & 25.3 & 16.1 & 25.1 & 14.8 & 11.8 & 14.7 & 10.8 & 12.7
\end{array}$

She uses the Mann-Whitney U test and a significance level of 0.05.This is a ______ test, and the critical ______.
A)one-tailed; value is 1.96
B)two-tailed; values are ±1.96
C)one-tailed; value is 1.645
D)two-tailed; values are ±1.645
E)one-tailed; value is $\pm$1.96

Question

A researcher wants to determine whether the means of two independent populations are the same.She has two independent random samples, one from each population, shown in the following table:  $\quad $ $\quad $ $\quad $ $\quad $Sample I $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $Sample II
$\begin{array}{llll|lllll}
\hline 11.5 & 15.7 & 22.8 & 22.5 & 12.6 & 13.8 & 17.5 & 10.7 & 13.5 \
12.4 & 25.3 & 16.1 & 25.1 & 14.8 & 11.8 & 14.7 & 10.8 & 12.7
\end{array}$

She uses the Mann-Whitney U test and a significance level of 0.05.This is a ______ test, and the critical ______.
A)one-tailed; value is 1.96
B)two-tailed; values are ±1.96
C)one-tailed; value is 1.645
D)two-tailed; values are ±1.645
E)one-tailed; value is $\pm$1.96

Quizplus · Accepted Answer

The Mann-Whitney U test is a non-parametric test used to compare differences between two independent groups when the assumptions for the t-test are not met. It is typically used as a two-tailed test because the researcher is interested in determining whether there is a difference in the medians of the two groups, not necessarily in a specific direction of the difference. The critical values mentioned (±1.96) correspond to a 95% confidence level (or a significance level of 0.05) for a two-tailed normal distribution, which is a common framework for interpreting the results of such tests, although the specific critical values for the Mann-Whitney U test depend on sample size and are not directly equivalent to z-values.

A Researcher Wants to Determine Whether the Means of Two \quad

A Researcher Wants to Determine Whether the Means of Two $\quad$