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To Discourage Cheating, a Professor Makes Three Different Versions of an Exam

question 10

Essay

To discourage cheating, a professor makes three different versions of an exam. For the 105
students in her class, she makes 35 copies of each version. The 105 exams are randomly
scrambled, and one copy is given to each student. After the exam, the professor is
concerned that one version might have been easier than the others. She uses a one-way
ANOVA to test whether the average score was different for the three versions. The
ANOVA table and a boxplot of the results are below. $\begin{array} { | l | r | c | r | c | c | } \hline \text { Source } & \text { df } & \begin{array} { c } \text { Sums of } \\\text { Squares }\end{array} & \begin{array} { c } \text { Mean } \\\text { Square }\end{array} & \text { F-ratio } & \text { P-value } \\\hline \text { Version } & 2 & 771.943 & 385.971 & 4.4317 & 0.0143 \\\hline \text { Error } & 102 & 8883.49 & 87.093 & & \\\hline \text { Total } & 104 & 9655.43 & & & \\\hline\end{array}$
$To discourage cheating, a professor makes three different versions of an exam. For the 105 students in her class, she makes 35 copies of each version. The 105 exams are randomly scrambled, and one copy is given to each student. After the exam, the professor is concerned that one version might have been easier than the others. She uses a one-way ANOVA to test whether the average score was different for the three versions. The ANOVA table and a boxplot of the results are below. \begin{array} { | l | r | c | r | c | c | } \hline \text { Source } & \text { df } & \begin{array} { c } \text { Sums of } \\ \text { Squares } \end{array} & \begin{array} { c } \text { Mean } \\ \text { Square } \end{array} & \text { F-ratio } & \text { P-value } \\ \hline \text { Version } & 2 & 771.943 & 385.971 & 4.4317 & 0.0143 \\ \hline \text { Error } & 102 & 8883.49 & 87.093 & & \\ \hline \text { Total } & 104 & 9655.43 & & & \\ \hline \end{array} a. What hypotheses are tested by this ANOVA? b. Write a sentence describing the conclusion of the test in the context of this problem. c. Use the plots below to check the ANOVA conditions.$

a. What hypotheses are tested by this ANOVA?
b. Write a sentence describing the conclusion of the test in the context of this problem.
c. Use the plots below to check the ANOVA conditions.

$To discourage cheating, a professor makes three different versions of an exam. For the 105 students in her class, she makes 35 copies of each version. The 105 exams are randomly scrambled, and one copy is given to each student. After the exam, the professor is concerned that one version might have been easier than the others. She uses a one-way ANOVA to test whether the average score was different for the three versions. The ANOVA table and a boxplot of the results are below. \begin{array} { | l | r | c | r | c | c | } \hline \text { Source } & \text { df } & \begin{array} { c } \text { Sums of } \\ \text { Squares } \end{array} & \begin{array} { c } \text { Mean } \\ \text { Square } \end{array} & \text { F-ratio } & \text { P-value } \\ \hline \text { Version } & 2 & 771.943 & 385.971 & 4.4317 & 0.0143 \\ \hline \text { Error } & 102 & 8883.49 & 87.093 & & \\ \hline \text { Total } & 104 & 9655.43 & & & \\ \hline \end{array} a. What hypotheses are tested by this ANOVA? b. Write a sentence describing the conclusion of the test in the context of this problem. c. Use the plots below to check the ANOVA conditions.$

Definitions:

Delirium

An acute, often reversible, mental disorder characterized by confused thinking, lack of awareness of the environment, and cognitive disturbances.

Perceptual Alterations

Changes or distortions in the way individuals perceive reality, often experienced in certain mental health conditions, affecting sensory experiences or interpretation of the environment.

Disturbed Orientation

A condition in which an individual has trouble recognizing time, place, situation, or personal identity.

Fluctuating Levels

Variations or changes in intensity, quantity, or value of something over a period of time.