(Solved) A teacher wants to see if two different forms of an exam are equivalent or if one of the exams is ...

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A teacher wants to see if two different forms of an exam are equivalent or if one of the exams is ...

A teacher wants to see if two different forms of an exam are equivalent or if one of the exams is more difficult than the other. She has 120 students, which she randomly sorts into two groups of 60. The group that that takes exam A has a mean score of 78.1% with a standard deviation of 5.6%. Exam B scores an average of 74.8% with a standard deviation of 8.7%.

Do these scores provide convincing statistical evidence that there is a difference in the difficulty of the two exams?

Textbook

Stats: Modeling the World

Edition: 4^th

Authors: Bock, Velleman, De Veaux

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zar

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4 years ago

A teacher wants to see if two different forms of an exam are equivalent or if one of the exams is more difficult than the other. She has 120 students, which she randomly sorts into two groups of 60. The group that that takes exam A has a mean score of 78.1% with a standard deviation of 5.6%. Exam B scores an average of 74.8% with a standard deviation of 8.7%.

Find and interpret a 95% confidence interval. Also explain how the values of your confidence interval correspond with your conclusion on #1.

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rinderbik

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4 years ago

(78.1- 74.8) ± t*SE = (0.65, 5.95)
We are 95% confident that the true mean difference between exam A and B is 0.65% to 5.95% higher for A vs. B. This confirms our result in #1, as it shows that exam A is different than exam B by at least a small amount. Since we rejected H₀, we expected to see a confidence interval that did not contain zero.

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zar

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4 years ago

Thanks

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