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# An Analysis of Variance Question

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Do students at various universities differ in how sociable they are? Twenty-five students were randomly selected from each of three universities in a region and were asked to report on the amount of time they spent socializing each day with other students.

The result for University X was a mean of 5 hours and an estimated population variance of 2 hours.
For University Y, M= 4, s^2 = 1.5.
Finally, for University Z, M = 6, s^2 = 2.5.

What should you conclude? Use the .05 level.
(a) Use the steps of hypothesis testing,
(b) figure the effect size for the study; and
(c) explain your answers to parts (a) and (b) to someone who has never had a course in statistics.

https://brainmass.com/statistics/analysis-of-variance/analysis-variance-question-473058

#### Solution Preview

Please see the attachment for the solution.
So to summarize, here's what you have:
X Y Z
Sample Mean, 5 4 6
Sample Variance, 2 1.5 2.5
Sample Size, 25 25 25

Preliminary Calculations for the ANOVA Test:

1.
2.
3.
4.
An ANOVA hypothesis test tests the claim that the population mean values are NOT significantly different against the claim that at least one of them IS significantly ...

#### Solution Summary

This solution examines whether or not the sociability levels of students at three different universities are significantly different from one another, using an analysis of variance test (ANOVA) to statistically assess this question. The solution demonstrates the steps of hypothesis testing, explains how to find the effect size and interpret it, and explains the entire process in layman's terms.

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