Assignment:
In many of the assignments, I have tried to guide you step-by-step through various types of problems. What I want to do here is throw you into the shoes of a researcher ... someone is unloading a large amount of data on you, and it will be your job to sift through it to draw some conclusions. My hope is that as you work through this, you can pull together / make connections between the things you have learned, and that you discover that you are able to apply the concepts we have studied.
For some questions, there is a variety of possible answers. What I am most interested in is your thought process, what tools you decide to use, and how you use those tools. So long as you can provide a statistically valid justification (including supporting Minitab graphs/output) for your answers, you are correct. You are welcome to provide hand computations wherever you feel more comfortable with them, but I would encourage you to use the power of Minitab wherever possible. Show your work by either providing your hand computations using Equation Editor OR by pasting your Minitab output into this document.
Below is data for 12 National League baseball teams from 2010. The same data can be found in the MAT1540GenEd.mtw file, which is located on the Unit 3 Mini-Project page of our course.
|
Team
|
Winning Percentage
|
Runs
|
Home Runs
|
Team Batting Average
|
On Base Percentage
|
Batting Average Against
|
Team ERA
|
|
Philadelphia
|
0.599
|
772
|
166
|
0.260
|
0.332
|
0.254
|
3.67
|
|
Atlanta
|
0.562
|
738
|
139
|
0.258
|
0.339
|
0.246
|
3.56
|
|
San Francisco
|
0.568
|
697
|
162
|
0.257
|
0.321
|
0.236
|
3.36
|
|
Chicago Cubs
|
0.463
|
685
|
149
|
0.257
|
0.320
|
0.255
|
4.18
|
|
Florida
|
0.494
|
719
|
152
|
0.254
|
0.321
|
0.261
|
4.08
|
|
LA Dodgers
|
0.494
|
667
|
120
|
0.252
|
0.322
|
0.244
|
4.01
|
|
Washington
|
0.426
|
655
|
149
|
0.250
|
0.318
|
0.266
|
4.13
|
|
Arizona
|
0.401
|
713
|
180
|
0.250
|
0.325
|
0.271
|
4.81
|
|
NY Mets
|
0.488
|
656
|
128
|
0.249
|
0.314
|
0.260
|
3.70
|
|
Houston
|
0.469
|
611
|
108
|
0.247
|
0.303
|
0.261
|
4.09
|
|
San Diego
|
0.556
|
665
|
132
|
0.246
|
0.317
|
0.240
|
3.39
|
|
Pittsburgh
|
0.352
|
587
|
126
|
0.242
|
0.304
|
0.282
|
5.00
|
Some of these variables make better predictor variables and some make better response variables. Spend some time thinking about what you suspect could be pairs of response and explanatory (predictor) variables.
Justify your answers below with the appropriate statistical information when needed.
1) For which pair of variables is a least squares regression model inappropriate?
2) Now focus on a pair of variables that is best fit for a least squares regression model/equation
a) How did you decide on this pair of variables?
b) Which variable should be the explanatory variable, and which should be the response variable? Explain your choices.
c) What is the least squares regression model and what statistical support do you have that this model has any value?
3) Consider your least squares regression model/equation.
a) Interpret the slope of your model.
b) Interpret the intercept of your model, and if the interpretation is inappropriate, explain why.
c) Between what two values of the predictor variable is your model valid?
d) Explain why extrapolation (using values outside of the scope of the model) could be dangerous.
e) Give a specific example of a prediction that could be made with your model, and interpret your answer.
f) Describe any other limitations of your model.
Heights Analysis
(Paraphrased from Just the Essentials by Johnson/Kuby) The average height for an early 17th-century English woman was about 60.5 inches. While average heights in England remained virtually unchanged in the 17th and 18th centuries, American colonists grew taller.
The main reasons for this difference are improved nutrition, notably increased consumption of meat and milk, and antibiotics. The National Center for Health Statistics (NCHS) provides statistical information that will guide actions and policies to improve the health of the American people. Recent data from the NCHS give the average height of women in the United States as µ = 63.7 inches.
Download and open the data file heights.mtw from the Unit 3 Mini-Project page of our course. This file contains the heights of 50 randomly selected women from the health profession. At the a = 10% level, does this data indicate that there is a difference between the average heights of women in the health profession and women in the general U.S. population? If so, provide and interpret an appropriate confidence interval for the average height of women in the health profession.
Include and label all the steps of your analysis, and justify all of your answers with the appropriate statistical information.
Sprinkler System Analysis
Your company produces fire-prevention sprinkler systems. The average activation time for the systems is supposed to be about 25 seconds, and you should be quite concerned if the average activation time is significantly more than 25 seconds. The manager has asked you to test a random sample of 13 systems and report back - does your company have cause for concern? Download and open the data file sprinkler.mtw (from the Unit 3 Mini-Project page of our course) to find the data on the activation time (in seconds) for your sample. Use a = 5%.
Include and label all the steps of your analysis, and justify all of your answers with the appropriate statistical information.