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# Analysis of variance

ANOVA: Degrees of freedom and the F statistic
Jointsoft is a great over-the-counter arthritis medication, but who will ever know about it? Unfortunately, many people with arthritis tend to be elderly and rather immobile, so advertisers of arthritis medications face limitations in ways to get their messages across. Currently, their best modes of advertisement are commercials on daytime TV, advertisements in select magazines, fliers in convalescent homes, and (believe it or not) advertisements on certain Web pages.
Marketing managers for Jointsoft are investigating these four modes of advertisement in four small communities (with a different mode of advertisement in each community). The marketing managers have selected days at random and are looking at the daily sales (in dollars) in each of the communities on each of these days. Here is what they have to work with:
Groups Sample Size Sample Mean Sample Variance
TV 30 567.5 2982.3
Magazines 30 587.9 3525.3
Fliers 30 590.7 2072.0
Web Pages 30 571.1 2360.3

Suppose that the marketing managers perform a one-way, independent-samples ANOVA test to decide if there are differences in the mean daily sales arising from the four modes of advertisement. (So, they're assuming that the only difference among the four communities is the mode of advertisement used in it.) Such a test uses the statistic

Variation between the samples .

Variation within the samples

For the information in the chart above, .

Give the numerator degrees of freedom of this F statistic.

Give the denominator degrees of freedom of this F statistic.

#### Solution Summary

The solution provides step by step method for the calculation of ANOVA model . Formula for the calculation and Interpretations of the results are also included.

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