Jointsoft is a great over-the-counter arthritis medication, but who will ever know about it? Unfortunately, many...

 

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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 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 30 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. Sample Sample Sample size Groups mean variance TV 30 547.4 2372.3 Magazines 30 586.4 2274.3 Fliers 30 564.6 2344.1 Web pages 30 577.5 1981.8 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 following statistic. Variation between the samples F = Variation within the samples For the information in the chart above,F = 3.84. (a) Give the p-value corresponding to this value of the F statistic. Round your answer to at least three decimal places. (b) 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 the others? O Yes O No 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 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 30 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. Sample Sample Sample size Groups mean variance TV 30 547.4 2372.3 Magazines 30 586.4 2274.3 Fliers 30 564.6 2344.1 Web pages 30 577.5 1981.8 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 following statistic. Variation between the samples F = Variation within the samples For the information in the chart above,F = 3.84. (a) Give the p-value corresponding to this value of the F statistic. Round your answer to at least three decimal places. (b) 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 the others? O Yes O No