APPLIED STAT.IN BUS.+ECONOMICS
APPLIED STAT.IN BUS.+ECONOMICS
6th Edition
ISBN: 9781259957598
Author: DOANE
Publisher: RENT MCG
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Chapter 15.1, Problem 1SE

Instructions: For each exercise, include software results (e.g., from Excel, MegaStat, or JMP) to support your chi-square calculations. (a) State the hypotheses. (b) Show how the degrees of freedom are calculated for the contingency table. (c) Using the level of significance specified in the exercise, find the critical value of chi-square from Appendix E or from Excel’s function =CHISQ.INV.RT(alpha, deg_freedom). (d) Carry out the calculations for a chi-square test for independence and draw a conclusion. (e) Which cells of the contingency table contribute the most to the chi-square test statistic? (f) Are any of the expected frequencies too small? (g) Interpret the p-value. If necessary, you can calculate the p-value using Excel’s function =CHISQ.DIST.RT(test statistic, deg_freedom). *(h) If it is a 2 × 2 table, perform a two-tailed, two-sample z test for π1 = π2 and verify that z2 is the same as your chi-square statistic. Note: Exercises marked with an asterisk (*) are more difficult.

15.1 A random sample of California residents who had recently visited a car dealership were asked which type of vehicle they were most likely to purchase, with the results shown. Research question: At α = .10, is the choice of vehicle type independent of the buyer’s age?

Chapter 15.1, Problem 1SE, Instructions: For each exercise, include software results (e.g., from Excel, MegaStat, or JMP) to

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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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APPLIED STAT.IN BUS.+ECONOMICS

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