Math 207 Homework Assignment 3

Due Friday, October 8 (beginning of class)

 

NOTES: As mentioned in the last homework assignment, I expect your homework solutions to be thorough, well-written (use context and complete sentences), neat, complete (thoughtfully answer all parts of the question), well-labeled (clearly label each problem and give all graphs appropriate titles), stapled, and in your own words/explanations (re: Honor Code). For the counting-method problems, include a sentence of reasoning for each part of your answer (e.g., for each combination or permutation you include). In general, the argumentation and organization of your solutions must be thorough and clear.

 

As last time, the Minitab files needed to do the homework are on the math_207 share folder (in the Homework Data subfolder—U:\Class_Share\Math\math_207\Homework Data). Be sure to copy these files into your personal account (do not simply use the files directly from the share folder).

 

Six Textbook Problems (please read the additional notes carefully):

3.30 (use Minitab)

4.38 (use counting methods to solve the problem, carefully explain each part of your method, and, in the end, determine the actual probability value—that is, do not leave your answer in un-simplified terms)

4.39 (Assume the shapes are distinct—e.g., assume each of the three like shapes is a different color. Use counting methods to solve the problem, carefully explain each part of your method, and, in the end, determine the actual probability value—that is, do not leave your answer in un-simplified terms)

4.62

4.114

4.125

 

Additional Problem 1 (use Minitab):

This data set (in the share folder) shows the prices (in dollars) and sizes (in inches) of ten LCD standard definition TVs in the 14- to 20-inch category (data provided by Consumer Reports). Suppose a Best Buy employee wants to predict the price of a TV based on its screen size.

 

  1. Perform a linear regression of price on screen size—include a graph of the fitted line plot from Minitab.

 

  1. Create (and include) a basic residual plot (residuals versus explanatory variable) for the regression in part a. The regression line doesn’t completely capture the overall relationship in the data. How does the residual plot show this?

 

  1. Fit a quadratic model to the data (in the Fitted-Line-Plot dialog box, select “quadratic”), and include the graph. Does the value of  improve from the straight-line model to the quadratic model?

 

  1. Suppose the Best Buy employee asked you to predict the price of a 30-inch screen LCD standard definition TV—what would you tell him?

 

Additional Problem 2

Suppose a fair coin is flipped three times and the sequence of heads and tails is recorded. Let A = {heads on the first flip} and B = {exactly two heads in the three flips}. Are the events A and B independent? Use the definition of independence (not your intuition) and show your work. (It’s helpful to write out the sample space of the experiment. Remember the experiment consists of three flips of the coin.)