AP Statistics Homework 11. Logistic Regression

Transcription

1 AP Statistics Homework 11 Logistic Regression 1. Anabolic steroid abuse has been increasing despite increased press reports of adverse medical and psychiatric consequences. In a recent study, medical researchers studied the potential for addiction to testosterone in hamsters (Neuroscience [2004]: ). Hamsters were allowed to self-administer testosterone over a period of days, resulting in the death of some of the animals. The data below show the proportion of hamsters surviving versus the peak self-administration of testosterone (μg). Fit a logistic regression equation and use the equation to predict the probability of survival for a hamster with a peak intake of 40 μg. (Hint: See Examples 5.24 and 5.25)

2 2. Does high school GPA predict success in first-year college English? The proportion with a grade of C or better in freshman English for students with various high school GPAs for freshmen at Cal Poly, San Luis Obispo, in fall of 2007 is summarized in the accompanying table. Fit a logistic regression equation that would allow you to predict the probability of passing freshman English based on high school GPA. Use the resulting equation to predict the probability of passing freshman English for students with a high school GPA of 2.2. High School GPA % C or Better p 1 p y = ln ( p 1 p )

3 Chapter Define the term chance experiment, and give an example of a chance experiment with four possible outcomes. 4. Define the term sample space, and then give the sample space for the chance experiment you described in the previous problem. 5. Consider the chance experiment in which the type of transmission automatic (A) or manual (M) is recorded for each of the next two cars purchased from a certain dealer. a. What is the set of all possible outcomes (the sample space)? b. Display the possible outcomes in a tree diagram. c. List the outcomes in each of the following events. Which of these events are simple events? B) the event that at least one car has an automatic transmission C) the event that exactly one car has an automatic transmission D) the event that neither car has an automatic transmission

4 d. What outcomes are in the event B and C? In the event B or C? 6. A new model of laptop computer can be ordered with one of three screen sizes (10 inches, 12 inches, 15 inches) and one of four hard drive sizes (50 GB, 100 GB, 150 GB, and 200 GB). Consider the chance experiment in which a laptop order is selected and the screen size and hard drive size are recorded. a. Display possible outcomes using a tree diagram. b. Let A be the event that the order is for a laptop with a screen size of 12 inches or smaller. Let B be the event that the order is for a laptop with a hard drive size of at most 100 GB. List the outcomes are in i. A c ii. A B iii. A B c. Let C denote the event that the order is for a laptop with a 200 GB hard drive. Are A and C mutually exclusive events? Are B and C mutually exclusive?

5 7. Suppose that, starting at a certain time, batteries coming off an assembly line are examined one by one to see whether they are defective (let D = defective and N = not defective). The chance experiment terminates as soon as a nondefective battery is obtained. a. Give five possible outcomes for this chance experiment. b. What can be said about the number of outcomes in the sample space? c. What outcomes are in the event E, that the number of batteries examined is an even number? 8. An engineering construction firm is currently working on power plants at three different sites. Define events E 1, E 2, and E 3 as follows: E 1 = the plant at Site 1 is completed by the contract date E 2 = the plant at Site 2 is completed by the contract date E 3 = the plant at Site 3 is completed by the contract date The following Venn diagram pictures the relationship among these events:

6 Shade the region in the Venn diagram corresponding to each of the following events. Redraw the Venn diagram for each part of the problem (otherwise you would be coloring over the same diagram). a. At least one plant is completed by the contract date. b. All plants are completed by the contract date. c. None of the plants are completed by the contract date. d. Exactly one of the three plants is completed by the contract date. e. Either the plant at Site 1 or both of the other two plants are completed by the contract date.