Statistics for Psychology
Statistics for Psychology
6th Edition
ISBN: 9780205258154
Author: Arthur Aron Ph.D., Elaine N. Aron Ph.D., Elliot Coups Ph.D., Cole Publishing
Publisher: PEARSON
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Chapter 9, Problem 5.5HD
To determine

Check whether the test is significant or not for the given information.

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1- Let A = {A1, A2, ...), in which A, A, = 0, when i j. a) Is A a π-system? If not, which element(s) should be added to A to become a π-system? b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such class; prove that F is a σ-filed containing A.) c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you construct a probability measure on σ(A)? (Hint: use extension theorem.) 2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
In a town with 5000 adults, a sample of 50 is selected using SRSWOR and asked their opinion of a proposed municipal project; 30 are found to favor it and 20 oppose it. If, in fact, the adults of the town were equally divided on the proposal, what would be the probability of observing what has been observed? Approximate using the Binomial distribution. Compare this with the exact probability which is 0.0418.
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