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. Marketing managers for Jointsoft are investigating several modes of advertisement in several small communities (with a different mode of advertisement being investigated in each community). The marketing managers have selected a collection of days at random and are looking at the daily Jointsoft sales (in dollars) in each of the communities on each of these days. 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. (Thus, they're assuming that the only difference among the four communities is the mode of advertisement used in it.) (a)The results of the ANOVA test are summarized in the ANOVA table below. Fill in the missing value in the ANOVA table. (round your answer to at least two decimal places) Source of variationDegrees of freedomSum of squaresMean squareF statisticTreatments(between groups)318,948.846316.28 Error(within groups)188452,1872405.25 Total191471,135.84 (a) The v ts of the ANOVA test are summarized in the ANOVA table below. Fill in the missing value in the ANOVA table. (round your answer to at least twodeciniai places)Source ofDegrees ofSum ofMean square F statisticvariationfreedomsquaresTreatments(betweengroups)318,948.846316.28Error(withingroups)188452,1872405.25Total191471,135.84(b) How many modes of advertisement were studied?(c) For the ANOVA test, it is assumed that the population variances of daily sales are equal for each mode of advertisement studied. What is an unbiasedestimate of this common population variance based on the sample variances?(d) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places.(e) Using the 0.01 level of significance, can the marketing managers conclude that the mean daily sales arising fromleast one of the modes of advertisementdiffers from that of the others?

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Description: 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 thei

Answered: (a) The v ts of the ANOVA test are…

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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. Marketing managers for Jointsoft are investigating several modes of advertisement in several small communities (with a different mode of advertisement being investigated in each community). The marketing managers have selected a collection of days at random and are looking at the daily Jointsoft sales (in dollars) in each of the communities on each of these days.

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. (Thus, they're assuming that the only difference among the four communities is the mode of advertisement used in it.)

(a)The results of the ANOVA test are summarized in the ANOVA table below. Fill in the missing value in the ANOVA table. (round your answer to at least two decimal places)

Source of variation	Degrees of freedom	Sum of squares	Mean square
Treatments (between groups)	3	18,948.84	6316.28
Error (within groups)	188	452,187	2405.25
Total	191	471,135.84

(a) The v ts of the ANOVA test are summarized in the ANOVA table below. Fill in the missing value in the ANOVA table. (round your answer to at least two
deciniai places)
Source of
Degrees of
Sum of
Mean square F statistic
variation
freedom
squares
Treatments
(between
groups)
3
18,948.84
6316.28
Error
(within
groups)
188
452,187
2405.25
Total
191
471,135.84
(b) How many modes of advertisement were studied?
(c) For the ANOVA test, it is assumed that the population variances of daily sales are equal for each mode of advertisement studied. What is an unbiased
estimate of this common population variance based on the sample variances?
(d) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places.
(e) Using the 0.01 level of significance, can the marketing managers conclude that the mean daily sales arising from
least one of the modes of advertisement
differs from that of the others?

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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