of n, randomly selected male smokers, X, smoked filter cigarettes, whereas of n, randomly selected female smokers, X, smoked filter cigarette robabilities that a randomly selected male and female, respectively, smoke filter cigarettes. (a) Show that (X,/n,) – (X,/n,) is an unbiased estimator for p, - P2. [Hint: E(X;) = np, for i = 1, 2.] X1 1 n2 n2 n2 = P1- P2 (b) What is the standard error of the estimator in part (a)? P1(1-P1 P2(1-P2) n2 (c) How would you use the observed values x, and x, to estimate the standard error of your estimator? O You would put them directly into the formula to obtain the estimate of the standard error. O You would use them to estimate the necessary quantities and then put these into the formula. O You can not use the observed values to estimate the standard error of your estimator. O There is not enough information. (d) If n, = n, = 200, x, = 126, and x, = 164, use the estimator of part (a) to obtain an estimate of p, - P2. (Round your answer to thr -0.19 (e) Use the result of part (c) and the data of part (d) to estimate the standard error of the estimator. (Round your answer to three decim 0.041
of n, randomly selected male smokers, X, smoked filter cigarettes, whereas of n, randomly selected female smokers, X, smoked filter cigarette robabilities that a randomly selected male and female, respectively, smoke filter cigarettes. (a) Show that (X,/n,) – (X,/n,) is an unbiased estimator for p, - P2. [Hint: E(X;) = np, for i = 1, 2.] X1 1 n2 n2 n2 = P1- P2 (b) What is the standard error of the estimator in part (a)? P1(1-P1 P2(1-P2) n2 (c) How would you use the observed values x, and x, to estimate the standard error of your estimator? O You would put them directly into the formula to obtain the estimate of the standard error. O You would use them to estimate the necessary quantities and then put these into the formula. O You can not use the observed values to estimate the standard error of your estimator. O There is not enough information. (d) If n, = n, = 200, x, = 126, and x, = 164, use the estimator of part (a) to obtain an estimate of p, - P2. (Round your answer to thr -0.19 (e) Use the result of part (c) and the data of part (d) to estimate the standard error of the estimator. (Round your answer to three decim 0.041
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I am having a tought time with this question
![Of n, randomly selected male smokers, X, smoked filter cigarettes, whereas of n, randomly selected female smokers, X, smoked filter cigarettes. Let p, and p, denote the
probabilities that a randomly selected male and female, respectively, smoke filter cigarettes.
(a) Show that (X,/n,) - (X2/n,) is an unbiased estimator for p, - P2. [Hint: E(X;) = np, for i = 1, 2.]
E( X1
E( X2
n1
n2
n2
1
1
=
n1
n2
= P1 - P2
(b) What is the standard error of the estimator in part (a)?
P1(1-P1)
Р
+
P2(1-P2)
(c) How would you use the observed values x, and x, to estimate the standard error of your estimator?
O You would put them directly into the formula to obtain the estimate of the standard error.
O You would use them to estimate the necessary quantities and then put these into the formula.
O You can not use the observed values to estimate the standard error of your estimator.
O There is not enough information.
(d) If n, = n, = 200, x, = 126, and x, = 164, use the estimator of part (a) to obtain an estimate of p, - P2. (Round your answer to three decimal places.)
|-0.19
(e) Use the result of part (c) and the data of part (d) to estimate the standard error of the estimator. (Round your answer to three decimal places.)
0.041](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86bfc21f-7304-4d6a-8ae3-de059a5180e7%2Fde9b99a9-28e3-4932-8765-0b0011b6fd07%2F8jawxd_processed.png&w=3840&q=75)
Transcribed Image Text:Of n, randomly selected male smokers, X, smoked filter cigarettes, whereas of n, randomly selected female smokers, X, smoked filter cigarettes. Let p, and p, denote the
probabilities that a randomly selected male and female, respectively, smoke filter cigarettes.
(a) Show that (X,/n,) - (X2/n,) is an unbiased estimator for p, - P2. [Hint: E(X;) = np, for i = 1, 2.]
E( X1
E( X2
n1
n2
n2
1
1
=
n1
n2
= P1 - P2
(b) What is the standard error of the estimator in part (a)?
P1(1-P1)
Р
+
P2(1-P2)
(c) How would you use the observed values x, and x, to estimate the standard error of your estimator?
O You would put them directly into the formula to obtain the estimate of the standard error.
O You would use them to estimate the necessary quantities and then put these into the formula.
O You can not use the observed values to estimate the standard error of your estimator.
O There is not enough information.
(d) If n, = n, = 200, x, = 126, and x, = 164, use the estimator of part (a) to obtain an estimate of p, - P2. (Round your answer to three decimal places.)
|-0.19
(e) Use the result of part (c) and the data of part (d) to estimate the standard error of the estimator. (Round your answer to three decimal places.)
0.041
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