Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 6.1, Problem 11E
Of n1 randomly selected male smokers, X1 smoked filter cigarettes, whereas of n2 randomly selected female smokers. X2 smoked filter cigarettes. Let p1 and p2 denote the probabilities that a randomly selected male and female, respectively, smoke filter cigarettes.
- a. Show that (X1/n1) - (X2/n2) is an unbiased estimator for p1 - p2. [Hint: E(X) = nipi for i = 1, 2.]
- b. What is the standard error of the estimator in part (a)?
- c. How would you use the observed values x1 and x2 to estimate the standard error of your estimator?
- d. If n1 = n2 = 200, x1 = 127, and x2 = 176, use the estimator of part (a) to obtain an estimate of p1 - p2.
- e. Use the result of part (c) and the data of part (d) to estimate the standard error of the estimator.
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Of n1 randomly selected male smokers, X1 smoked filter cigarettes, whereas of n2 randomly selected female smokers, X2 smoked filter cigarettes. Let p1 and p2 denote the probabilities that a randomly selected male and female, respectively, smoke filter cigarettes.
(a) Show that
(X1/n1) − (X2/n2) is an unbiased estimator for p1 − p2. [Hint: E(Xi) = nipi for i = 1, 2.]
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n2
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1
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1
n2
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1
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1
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p1 − p2
(b) What is the standard error of the estimator in part (a)?
(d) If n1 = n2 = 206, x1 = 134, and x2 = 165, use the estimator of part (a) to obtain an estimate of p1 − p2. (Round your answer to three decimal places.)
Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).
A pharmaceutical company has developed a new drug to help relieve acid reflux. However, as with all new drugs, there are concerns about adverse side effects. To check this, the company administers the drug to n randomly chosen people with acid reflux, and it finds that k of them experience adverse side effects. The company hopes to reject the null hypothesis that the proportion of drug-takers who experience adverse side effects is at least 0.5%. Which of the following is true?
a. If n=1,250 and k=1, this is enough evidence to reject the null at the 1% level.
b. If n=1,000 and k=3, this is enough evidence to reject the null at the 10% level.
c. If n=4,000 and k=9, this is enough evidence to reject the null at the 1% level.
d. If n=1,600 and k=4, this is enough evidence to reject the null at the 5% level.
Chapter 6 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 6.1 - The accompanying data on flexural strength (MPa)...Ch. 6.1 - The National Health and Nutrition Examination...Ch. 6.1 - Consider the following sample of observations on...Ch. 6.1 - The article from which the data in Exercise 1 was...Ch. 6.1 - As an example of a situation in which several...Ch. 6.1 - Urinary angiotensinogen (AGT) level is one...Ch. 6.1 - a. A random sample of 10 houses in a particular...Ch. 6.1 - In a random sample of 80 components of a certain...Ch. 6.1 - Each of 150 newly manufactured items is examined...Ch. 6.1 - Using a long rod that has length , you are going...
Ch. 6.1 - Of n1 randomly selected male smokers, X1 smoked...Ch. 6.1 - Suppose a certain type of fertilizer has an...Ch. 6.1 - Consider a random sample X1,..., Xn from the pdf...Ch. 6.1 - A sample of n captured Pandemonium jet fighters...Ch. 6.1 - Let X1, X2,..., Xn represent a random sample from...Ch. 6.1 - Suppose the true average growth of one type of...Ch. 6.1 - In Chapter 3, we defined a negative binomial rv as...Ch. 6.1 - Let X1, X2,..., Xn be a random sample from a pdf...Ch. 6.1 - An investigator wishes to estimate the proportion...Ch. 6.2 - A diagnostic test for a certain disease is applied...Ch. 6.2 - Let X have a Weibull distribution with parameters ...Ch. 6.2 - Let X denote the proportion of allotted time that...Ch. 6.2 - Let X represent the error in making a measurement...Ch. 6.2 - A vehicle with a particular defect in its emission...Ch. 6.2 - The shear strength of each of ten test spot welds...Ch. 6.2 - Consider randomly selecting n segments of pipe and...Ch. 6.2 - Let X1,..., Xn be a random sample from a gamma...Ch. 6.2 - Prob. 28ECh. 6.2 - Consider a random sample X1, X2,, Xn from the...Ch. 6.2 - At time t = 0, 20 identical components are tested....Ch. 6 - An estimator is said to be consistent if for any ...Ch. 6 - a. Let X1,.., Xn be a random sample from a uniform...Ch. 6 - At time t = 0, there is one individual alive in a...Ch. 6 - The mean squared error of an estimator is MSE ()...Ch. 6 - Prob. 35SECh. 6 - When the population distribution is normal, the...Ch. 6 - When the sample standard deviation S is based on a...Ch. 6 - Each of n specimens is to be weighed twice on the...
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