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.]E X1n1 − X2n2 =1n1E − 1n2E =1n1 − 1n2 =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.)

Introduction: Consider it to be a success if a smoker smoked filter cigarettes. For a sample of size…

Answered: Of n1 randomly selected male smokers,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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(X_i) = n_ip_i for i = 1, 2.]

X₁

n₁

−

X₂

n₂

n₁

−

n₂

n₁

−

n₂

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.)

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