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

question 660

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

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