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. $$\begin{array} { l l l l l l l l l l l l } \text { College A } & 3.2 & 4.0 & 2.4 & 2.6 & 2.0 & 1.8 & 1.3 & 0.0 & 0.5 & 1.4 & 2.9 \\ \hline \text { College B } & 2.4 & 1.9 & 0.3 & 0.8 & 2.8 & 3.0 & 3.1 & 3.1 & 3.1 & 3.5 & 3.5 \end{array}$$

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Definitions:

Cognitive Deficits

Impairments in mental processes such as thinking, memory, and reasoning.

Male Zygote

The initial cell formed when a male sperm cell fertilizes a female egg, containing genetic material from both parents, including a Y chromosome from the father.

Chromosome Configuration

The particular arrangement and number of chromosomes in a cell, which can affect genetic expression and traits.

Matched Pairs

A statistical method used in experiments where subjects are paired based on certain criteria, enhancing the comparability of the groups.