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Analyzing Grade Variance: Is it More than Usual? A Chi-Square Test
Chapter 8, Problem 10(choose chapter or problem)
A statistics professor is used to having a variance in his class grades of no more than 100. He feels that his current group of students is different, and so he examines a random sample of midterm grades (listed below.) At \(\alpha\) = 0.05, can it be concluded that the variance in grades exceeds 100?
\(\begin{array}{rrrrr}
92.3 & 89.4 & 76.9 & 65.2 & 49.1 \\
96.7 & 69.5 & 72.8 & 67.5 & 52.8 \\
88.5 & 79.2 & 72.9 & 68.7 & 75.8
\end{array}\)
Questions & Answers
QUESTION:
A statistics professor is used to having a variance in his class grades of no more than 100. He feels that his current group of students is different, and so he examines a random sample of midterm grades (listed below.) At \(\alpha\) = 0.05, can it be concluded that the variance in grades exceeds 100?
\(\begin{array}{rrrrr}
92.3 & 89.4 & 76.9 & 65.2 & 49.1 \\
96.7 & 69.5 & 72.8 & 67.5 & 52.8 \\
88.5 & 79.2 & 72.9 & 68.7 & 75.8
\end{array}\)
Step 1 of 3
Given:
The data is given as,
92.3, 89.4, 76.9, 65.2, 49.1, 96.7, 69.5, 72.8, 67.5, 52.8, 88.5, 79.2, 72.9, 68.7, 75.8
The hypotheses are,
Null hypothesis:
\(H_{0}: \sigma^{2}=100\)
Alternate hypothesis:
\(H_{1}: \sigma^{2}>100\) (claim)
Watch The Answer!
Analyzing Grade Variance: Is it More than Usual? A Chi-Square Test
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Discover the process of analyzing variance in midterm grades with a Chi-Square test. Understand the significance of high variance and its implications. Follow along as we assess a professor's suspicion about unusually varied student performance.