Description
The company Performance Tires plans to engage in direct mail advertising. It is currently in
negotiations to purchase a mailing list of the names of people who bought sports cars within
the last three years. The owner of the mailing list claims that sales generated by contacting
names on the list will more than pay for the cost of using the list. (Typically, a company
will not sell its list of contacts, but provides the mailing services. For example, the owner of
the list would handle addressing and mailing catalogs.)
Before it is willing to pay the asking price of $3 per name, the company obtains a random
sample of 225 names and addresses from the list in order to run a small experiment. It sends
promotional mailings to each of these customers. The company makes a profit of 20% on
the gross dollar of a sale (not including the $3 cost of the name). For example, if a customer
orders $100 worth of goods (i.e., gross dollar) the company makes a $20 profit. If we include
the cost of the name, the $20 profit reduces to a $17 profit. Your goal is this assignment is
to answer the question: Should the company purchase the mailing list?
Use the file “direct mail.xlsx.” The data in this file are the gross dollar values of individual
customer’s orders generated by the experimental mailing. To load an Excel file, load the
package tidyverse, then load the package readxl (if you’ve installed tidyverse, then this
package should already be installed; if it is not, then install it through the “Packages” panel
on RStudio). Use the function read excel() to upload this Excel file in R.
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1. Why would a company want to run an experiment? Why not just buy the list and see
what happens?
2. Why would the holder of the list agree to allow the potential purchaser to run an experiment?
3. If you wanted to run a hypothesis test on the profitability of the list at the α = 0.05
level, what would your hypotheses be? What does µ represent?
4. Identify the population, parameter, sample, and statistic in this scenario.
5. In your hypotheses in question 3, what would it mean to make a Type I error in this
context? What is the probability of making such an error?
6. With the data you will use to test your hypothesis, (a) construct a histogram, (b) compute summary statistics (minimum, median, mean, maximum, and standard deviation),
and (c) compute the fraction of people who bought nothing from Performance Tires.
Describe the shape of the data. Remember to include the units of measurement.
7. Check the assumptions for a one-sample t-test. Are they satisfied for this data? Explain
your answer.
8. Test the hypotheses you specified in question 3 and provide a recommendation to the
company. Remember to identify the test statistic, degrees of freedom, p-value, and
conclusion (don’t just show the output of your R code).
9. What is the probability of making a Type II error with your hypothesis test in question
3 if the average profit was actually $2?
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