|
STAtistics / Mr. Hansen |
Name: ______________________ |
Quest (50 points)
Consider the following data set for questions 1-5:
x y
3 18
4 20
5 21
6 22
7 22.5
8 22.7
9 23
10 23.2
12 23.1
14 23
17 24
22 23
24 23
1. Show that a linear model, an exponential model, and a
logarithmic model are all inappropriate. Give the 
equation in each case,
along with other suitable justification. (You are supposed to know what is
needed.) Use reverse side.
2. For the logarithmic model, what value of x is predicted when y = 19?
3. For the linear model, what value of y is predicted when x = 16? Show your work.
4. Let x represent annual poker revenue (in $thousands), and let y represent number of pounds of fish that Leisure Suit Larry eats in a calendar year. State the value of b1, the linear model’s slope, and interpret b1 in context.
5. Which model, linear or logarithmic, is worse? Explain clearly.
Does draxatine (a made-up substance) help both males and females increase their upper-body strength? That is the research question we seek to answer in questions 6-10. A total of 82 male and 65 female volunteer subjects, ranging in age from 17 to 19, are available for experimentation purposes. It is known that males have much greater upper body strength, on average, than females, regardless of whether or not they are taking a draxatine supplement.
6. Design an experiment to address the research question. Show how all three of the components of good experimental design have been incorporated. Use reverse side.
7. What is the technical reason that block design is desirable in many experiments? Use the word variance or the term standard deviation in your response.
8. What is the real-world, bottom-line reason that block design can be useful? In answering your question, explain exactly how the answer to #7 might translate into something that everyone (not merely statisticians) would care about.
9. Explain briefly why a placebo treatment would be essential in the draxatine study, even if the evaluation of upper-body strength is purely objective (e.g., bench press under controlled conditions).
10. Is double-blinding necessary in the draxatine study? Briefly state why you think it might or might not be required.