Perform the Required Hypothesis Test by Using a Mann-Whitney Test

question 39

Essay

Perform the required hypothesis test by using a Mann-Whitney test. Use a normal approximation for M. Find the meanand standard deviation of M, the value of M and of the test statistic, the critical value(s), and state your conclusion.
-Test whether the mean grade for students from college A differs from the mean grade for students from College B. Independent simple random samples of 11 students from College A and 11 students from College B are selected. Grades of the students are shown in the table. Use a 0.05 level of significance. $$\begin{array} { l l l l l l l l l l l l } \text { College A } & 3.2 & 4.0 & 2.4 & 2.6 & 2.0 & 1.8 & 1.3 & 0.0 & 0.5 & 1.4 & 2.9 \\ \hline \text { College B } & 2.4 & 1.9 & 0.3 & 0.8 & 2.8 & 3.0 & 3.1 & 3.1 & 3.1 & 3.5 & 3.5 \end{array}$$

---

Definitions:

Lower South

Geographical region of the United States, often referencing the states most dependent on slave labor and that seceded first during the Civil War.

Eighteenth Century

The period from 1701 to 1800 in the Gregorian calendar, marked by significant historical events, cultural shifts, and advancements in various fields such as science and philosophy.

Spain

A country on Europe's Iberian Peninsula known for its diverse culture, history, and contributions to art, music, and literature.

Black Town

Historically, a town or community predominantly inhabited by African Americans, often established by freed slaves during and after the period of slavery in the United States.