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# Comparing the Average Difference and Standard Deviation

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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 Summary

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

##### 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 ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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