In an effort to counteract student cheating, the professor of a large class created four versions of a midterm exam, distributing the four versions among the 344 students in the class, so that each version was given to 86 students. After the exam, the professor computed the following information about the scores (the exam was worth 200 points): Sample Sample Sample size Group mean variance Version A Version B Version C Version D 86 150.3 420.3 86 155.7 352.0 86 148.5 479.1 86 158.8 369.9 Send data to calculator Send data to Excel The professor is willing to assume that the populations of scores from which the above samples were drawn are approximately normally distributed and that each has the same mean and the same variance. Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place. (a) Give an estimate of this common population variance based on the variance of the sample means given. (b) Give an estimate of this common population variance by pooling the sample variances given.

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Author:Amos Gilat
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In an effort to counteract student cheating, the professor of a large class created four versions of a midterm exam, distributing the four versions among the 344 students in the class, so that each version was given to 86 students. After the exam, the professor computed the following information about the scores (the exam was worth 200 points):

| Group      | Sample size | Sample mean | Sample variance |
|------------|-------------|-------------|-----------------|
| Version A  | 86          | 150.3       | 420.3           |
| Version B  | 86          | 155.7       | 352.0           |
| Version C  | 86          | 148.5       | 479.1           |
| Version D  | 86          | 158.8       | 369.9           |

[Send data to calculator] [Send data to Excel]

The professor is willing to assume that the populations of scores from which the above samples were drawn are approximately normally distributed and that each has the same mean and the same variance.

Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.

(a) Give an estimate of this common population variance based on the variance of the sample means given.  
[Input Box]

(b) Give an estimate of this common population variance by pooling the sample variances given.  
[Input Box]

[Calculate Button] [Reset Button] [Help Button]
Transcribed Image Text:In an effort to counteract student cheating, the professor of a large class created four versions of a midterm exam, distributing the four versions among the 344 students in the class, so that each version was given to 86 students. After the exam, the professor computed the following information about the scores (the exam was worth 200 points): | Group | Sample size | Sample mean | Sample variance | |------------|-------------|-------------|-----------------| | Version A | 86 | 150.3 | 420.3 | | Version B | 86 | 155.7 | 352.0 | | Version C | 86 | 148.5 | 479.1 | | Version D | 86 | 158.8 | 369.9 | [Send data to calculator] [Send data to Excel] The professor is willing to assume that the populations of scores from which the above samples were drawn are approximately normally distributed and that each has the same mean and the same variance. Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place. (a) Give an estimate of this common population variance based on the variance of the sample means given. [Input Box] (b) Give an estimate of this common population variance by pooling the sample variances given. [Input Box] [Calculate Button] [Reset Button] [Help Button]
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