Mathematical and Technological Literacy I Assignment 1: Linear Modeling and Trendlines

1.  Stores such as Sam's Club and Price-Costco charge an annual membership fee of approximately $40.  As a member you can purchase products at lower prices, but typically in larger quantities than one buys at ordinary stores. Savings vary from product to product, but for this question, let us assume you can save $20 for every $100 dollars you spend at one of these stores compared to shopping elsewhere.

a.  Suppose you spend $100 dollars in one year at such a store.  Do you come out ahead? How much do you save (or lose?) compared to not having membership and paying full price?

b.  Create a table in Excel showing the amount you spend in the first column with the corresponding overall savings in the second column.  In the spend column, start with zero dollars and go up to $600 in increments of $100.  Paste the completed table in your Word document.

c.  How much do you have to spend at the store for it to be worthwhile for you to buy membership?

d. The amount you save (or lose) by buying membership is a linear function of how much you spend.  Explain why.

e.  What are the two variables in this function?  Assign each variable a letter. Write the linear equation for your savings as a function of how much you spend at the store.

f.  From the analysis above, one of the factors one should consider when deciding whether or not to join a store such Sam's Club or Price-Costco is whether or not you are going to going to spend a certain minimal amount at the store in a year. What other factors should you consider when deciding whether to become a member of Sam's Club or Price-Costco?

2. Open the file USTobacco_MostRecent.xls which contains data on the total amount of tobacco produced in the US.

a. Make an XY scatter plot of the data.  Add a linear trendline to your plot, including the equation and the R-squared value. Include it in your document.

b. Use the equation method and extended trendline method to predict the amount of tobacco produced in 2013.  Show both results in your Word document.

c. How much confidence do you have in your prediction? Why?  (Write a short paragraph using the language we learned in class.)

3.  Open the file Smoking_MostRecent.xls which contains data on the percent of the US adult population that smokes cigarettes.

a. Make X,Y scatter graph of the years and the total percentages (not male and female) and add a trendline.  Include the equation and R-squared value for the trendline.  Paste the resulting chart into your Word document.

b. Using your model (equation method) and the extended trendline method, predict the percentage of the total population that smokes in 2011.  Show both results in your Word document.

c.  How much faith do you have in your prediction?  (Write a short paragraph using the language we learned in class.)

d. Use your model to estimate what percentage of the total population smoked in 1953.  Do you have faith in this prediction?  Explain.

e. Use your model to estimate when 100% of the US population smoked.  How much faith do you have in this prediction?  Explain.

4.  Read the article "Obesity Study Looks Thin: Results Warn That Everyone in US Will Be Overweight by the Year 2048," by Carl Bialik (Wall Street Journal, Aug. 15, 2008, A11) and respond to the following questions.

a. In a brief paragraph, summarize the main point of the article.

b. In a brief paragraph, explain how the article relates the material on linear modeling that we have studied, giving at least one specific example from class.