Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 12.2, Problem 6E
Refer to Exercise 12.5. Consider two methods for selecting the dosages. Method 1 assigns three rats to the dosage x = 2 and three rats to x = 5. Method 2 equally spaces the dosages between x = 2 and x = 5 (x = 2, 2.6, 3.2, 3.8, 4.4, and 5.0). Suppose that σ is known and that the relationship between E(Y) and x is truly linear (see Chapter 11). If we use the data from both methods to construct confidence intervals for the slope β1, which method will yield the longer interval? How much longer is the longer interval? If we use method 2, approximately how many observations will be required to obtain an interval the same length as that obtained by the optimal assignment of method 1?
12.5 Suppose that we wish to study the effect of the stimulant digitalis on the blood pressure Y of rats over a dosage
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A study is made for a particular allergy medication in order to determine the length of relief it provides Y (in hours) in relation to the dosage of medication X (in mg). For this reason, ten patients were given different doses of the medication and were asked to report back when the medication seemed to wear off.
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(i) Draw a scatter diagram.
(ii) Calculate the product moment correlation coefficient and comment on your answer.
(iii) Construct the least squares regression line.
Consider the following two a.m. peak work trip generation models, estimated by household linear regression:
T = 0.62 + 3.1 X1 + 1.4 X2 R2= 0.590
(2.3) (7.1) (5.9)
T = 0.01 + 2.4 X1 + 1.2 Z1 + 4.0 Z2 R2= 0.598
(0.8) (4.2) (1.7) (3.1)
X1 = number of workers in the household
X2 = number of cars in the household,
Z1 is a dummy variable which takes the value 1 if the household has one car,
Z2 is a dummy variable which takes the value 1 if the household has two or more cars.
Compare the two models and choose the best. If a zone has 1000 households, of which 50% have no car, 35% have one car, and the rest have exactly two cars, estimate the total number of trips generated by this zone. Use the preferred trip generation model and assume that each household has an average of two workers
Chapter 12 Solutions
Mathematical Statistics with Applications
Ch. 12.2 - Suppose that you wish to compare the means for two...Ch. 12.2 - Refer to Exercise 12.1. Suppose that you allocate...Ch. 12.2 - Suppose, as in Exercise 12.1, that two populations...Ch. 12.2 - Refer to Exercise 12.3. How many observations are...Ch. 12.2 - Suppose that we wish to study the effect of the...Ch. 12.2 - Refer to Exercise 12.5. Consider two methods for...Ch. 12.2 - Refer to Exercise 12.5. Why might it be advisable...Ch. 12.2 - The standard error of the estimator 1 in a simple...Ch. 12.3 - Consider the data analyzed in Examples 12.2 and...Ch. 12.3 - Two computers often are compared by running a...
Ch. 12.3 - When Y1i, for i = 1, 2,, n, and Y2i, for i = 1,...Ch. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - A plant manager, in deciding whether to purchase a...Ch. 12.3 - Muck is the rich, highly organic type of soil that...Ch. 12.3 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Complete the assignment of treatments for the...Ch. 12 - Prob. 28SECh. 12 - Prob. 29SECh. 12 - Prob. 30SECh. 12 - Prob. 31SECh. 12 - Prob. 32SECh. 12 - Prob. 33SECh. 12 - Prob. 34SECh. 12 - The earths temperature affects seed germination,...Ch. 12 - An experiment was conducted to compare mean...Ch. 12 - Prob. 37SE
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