EBK STATISTICS FOR BUSINESS & ECONOMICS
12th Edition
ISBN: 9780100460461
Author: Anderson
Publisher: YUZU
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Chapter 18.4, Problem 26E
A sample of 15 consumers provided the following product ratings for three different products. Five consumers were randomly assigned to test and rate each product. Use the Kruskal-Wallis test and α = .05 to determine whether there is a significant difference among the ratings for the products.
| Product | ||
| A | B | C |
| 50 | 80 | 60 |
| 62 | 95 | 45 |
| 75 | 98 | 30 |
| 48 | 87 | 58 |
| 65 | 90 | 57 |
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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.
Chapter 18 Solutions
EBK STATISTICS FOR BUSINESS & ECONOMICS
Ch. 18.1 - The following hypothesis test is to be conducted....Ch. 18.1 - Ten individuals participated in a taste test...Ch. 18.1 - The median number of part-time employees at...Ch. 18.1 - Net assets for the 50 largest stock mutual funds...Ch. 18.1 - The median annual income of subscribers to...Ch. 18.1 - The median annual income for families living in...Ch. 18.1 - Prob. 7ECh. 18.1 - A Pew Research Center survey asked adults if their...Ch. 18.1 - A poll taken during the recession in 2008 asked...Ch. 18.1 - Prob. 10E
Ch. 18.1 - Competition in the personal computer market is...Ch. 18.2 - Two fuel additives are tested to determine their...Ch. 18.2 - A sample of 10 men was used in a study to test the...Ch. 18.2 - Percents of on-time arrivals for flights in the...Ch. 18.2 - A test was conducted for two overnight mail...Ch. 18.2 - The PGA Players Championship was held at the...Ch. 18.2 - The Scholastic Aptitude Test (SAT) consists of...Ch. 18.3 - Two fuel additives are being tested to determine...Ch. 18.3 - Samples of starting annual salaries for...Ch. 18.3 - The gap between the earnings of men and women with...Ch. 18.3 - Prob. 21ECh. 18.3 - Each year Bloomberg Businessweek publishes...Ch. 18.3 - Police records show the following numbers of daily...Ch. 18.3 - A certain brand of microwave oven was priced at 10...Ch. 18.3 - Prob. 25ECh. 18.4 - A sample of 15 consumers provided the following...Ch. 18.4 - Three admission test preparation programs are...Ch. 18.4 - Forty-minute workouts of one of the following...Ch. 18.4 - Cond Nast Traveler magazine conducts an annual...Ch. 18.4 - A large corporation sends many of its first-level...Ch. 18.4 - The better-selling candies are often high in...Ch. 18.5 - Consider the following set of rankings for a...Ch. 18.5 - Prob. 33ECh. 18.5 - Prob. 34ECh. 18.5 - A national study by Harris Interactive, Inc.,...Ch. 18.5 - Prob. 36ECh. 18.5 - A student organization surveyed both current...Ch. 18 - A survey asked the following question: Do you...Ch. 18 - Due to a recent decline in the housing market, the...Ch. 18 - Twelve homemakers were asked to estimate the...Ch. 18 - Prob. 41SECh. 18 - The following data are product weights for the...Ch. 18 - A client wants to determine whether there is a...Ch. 18 - Prob. 44SECh. 18 - Prob. 45SECh. 18 - Prob. 46SECh. 18 - Prob. 47SE
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