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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 50 553.5 2686.3
Magazines 50 577.6 2956.0
Fliers 50 573.1 2232.0
Web Pages 50 566.9 1842.8
The marketing managers are assuming that the only difference among the communities is the mode of advertisement used. The marketing managers perform an ANOVA test to decide if there are significant differences in the mean daily sales arising from the different modes of advertisement (the "groups"). The results of the ANOVA test are summarized in the partially filled ANOVA table below. Fill in the rest of the ANOVA table, and then answer the questions about the ANOVA test. (In the table, round your answers for the mean squares to at least one decimal place each, and round your answer for the F statistic to at least two decimal places.)
Source of Variation Degrees of Freedom Sum of Squares Mean Squares F statistic
Between Groups (Answer here) 16471.4 (Answer here) (Answer here)
Within Groups (Answer here) 476137.9 (Answer here)
Total (Answer here) 492609.3
1. What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places.
2. Using the 0.05 level of significance, can the marketing managers conclude that the mean daily sales arising from at least one of the modes of advertisement differs from that of the others? Yes or No?
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The following outlines the process of using an ANOVA to perform a hypothesis test.
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