Memorandum

To: Marketing Manager of Speedy Collection

From: Group 5

Date: October 18, 2016

Subject: Recommendation for the company’s slogan (Under 50 days or your money back)

This memo serves as a suggestion regarding the analysis we made on Speedy Collection’s new slogan. Due to the current competition between the collection services company, the marketing department of the company has suggested a slogan “Under 50 days or your money back!!!!”. We agree that this slogan can build the company’s integrity and gain customers’ trust because 50 days is a relatively long time for them to get their money back. Also, adopting this slogan will distinguish our company from competitors and establish a good reputation. However, it is our opinion that for the slogan to work well and aligned with the money-back guarantee program, we need to add a couple of terms and conditions for the slogan. We have analyzed the data given and come to the idea that this additional terms and conditions are needed. For the individual account, we recommend that the slogan can be applied only if the amount is less than $292. For the business account, we can apply the slogan only if the amount is larger than $350.

After analyzing the two groups of accounts, which are the individual and business account, we learned that there are conditions needed to be satisfied for the slogan to work. For the individual account, we can get the money back within 50 days if the amount is less than $292. We set the maximum price as accurate as possible so that we will not lose any money. For the business account, we can get the money back within 50 days if the amount is greater than $350. The initial minimum for the business account was $304, but we decided to raise the minimum so that the company can still make a profit.

We are confident that Speedy Collection will do a lot better if the slogan is applied, considering all the conditions we just made. Without the company’s capability to collect the money from both accounts (individual and business), the new slogan will put the Marketing manager of Speedy Collection in a fragile position instead. Thus, before the marketing department of the company decides to apply the slogan, these points needs to be taken seriously into account.

Regards,

Speedy Collection Accounting Department

Appendix

Business Account

Business Account Scattered Plot

      This scattered plot graph shows the relationship between days and amount for the business account. As we can see from the slope, it shows a strong negative linear correlation between those two variables.

Analysis for Business Account

Simple Regression Equation: Days = 95.46 - 0.15 * Amount

Explanations:

●      Independent variable: Amount

●      Dependent variable: Days

●      b0 = 95.46 suggests that when the amount is equal to zero, it will take 95.46 days to collect the money back

●      b1 = -0.15 suggests that for every one unit increase in the amount, the days to collect the money back will decrease by 0.15 days

Days = 95.46 - 0.15 * Amount

(Substitute 50 into Days)

50 = 95.46 - 0.15 * Amount

Amount = 303.07

Solution: Apply the slogan only if Amount > $304

Hypothesis Testing:

Ho: β1 = 0 (no linear relationship)

Ha: β1 ≠ 0

Test Statistic: T = -19.45

Decision Rule:

Reject Ho if |T| > t_{α/2, df}

19.45 > t_{0.1/2, 49}

19.45 > 1.677

Decision:

Reject Ho. We are 90% sure that there is a linear relationship between the amount of dollars and days collected.

Individual Account

Individual Account Scattered Plot

      This scattered plot graph shows the relationship between days and amount for the individual account. As we can see from the slope, it shows a strong positive linear correlation between those two variables.

Analysis for Individual Account

Simple Regression Equation: Days = 6.22 + 0.15 * Amount

Explanations:

●      Independent variable: Amount

●      Dependent variable: Days

●      b0 = 6.22 suggests that when the amount is equal to zero, it will take 95.46 days to collect the money back

●      b1 = 0.15 suggests that for every one unit increase in the amount, the days to collect the money back will increase by 0.15 days

Days = 6.22 + 0.15 * Amount

50 = 6.22 + 0.15 * Amount

Amount = 291.87

Solution: Apply the slogan only if the amount <$292

Hypothesis Testing

Ho: β1 = 0 (no linear relationship)

Ha: β1 ≠ 0

Test Statistic: T = 35.72

Decision Rule:

Reject Ho if |T| > t_{α/2, df}

35.72 > t_{0.1/2, 49}

35.72 > 1.677

Decision and Conclusion:

Reject Ho. We are 90% sure that there is a linear relationship between the amount of dollars and days collected.