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Comparing the Average Difference and Standard Deviation

While it cannot be denied that advertising impacts sales, it is also true that advertising is expensive and companies want to advertise in ways that have the greatest benefit for the amount of money spent. A company that sells snack food designs two different advertising strategies, one focusing on print media and the other on radio. It ran the campaigns in a total of 16 different cities, paired on population size and measured the sales ($1000) in the week directly following the beginning of the campaign. The data are given below: (see attached chart)

Print Sales Radio Sales
28.3 22.1
24.6 19.1
23.1 20.3
21.0 24.4
25.7 22.4
22.5 19.2
32.0 22.8
23.5 20.3
24.3 25.5
25.2 22.6
23.3 24.9
25.3 29.7
22.2 22.2
23.4 28.5
23.9 28.2
25.7 21.6

Average?
Standard deviation?

a) Calculate the differences in sales for each pair of cities

b)Based on these differences, do you think there is a difference in mean sales for the two types of advertising campaigns? Why or why not?

c) Calculate the average difference and the standard deviation of the differences

d) Set up the hypotheses to test whether there is a difference in mean sales due to type of advertising

e) Assuming that the data are normally distributed, at the 0.01 level of significance, what can you conclude?

Solution Preview

a) Calculate the differences in sales for each pair of cities

P_Sales 28.3 24.6 23.1 21.0 25.7 22.5 32.0 23.5 24.3 25.2 23.3 25.3 22.2 23.4 23.9 25.7
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R_Sales 22.1 19.1 20.3 24.4 22.4 19.2 22.8 20.3 25.5 22.6 24.9 29.7 22.2 28.5 28.2 ...

Solution Summary

The solution shows how to calculate the average and standard deviation of the differences in sales for a pair of cities.

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