Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Textbook Question

Chapter 15.3, Problem 7E

A psychological experiment was conducted to compare the lengths of response time (in seconds) for two different stimuli. To remove natural person-to-person variability in the responses, both stimuli were applied to each of nine subjects, thus permitting an analysis of the difference between response times within each person. The results are given in the following table.

Chapter 15.3, Problem 7E, A psychological experiment was conducted to compare the lengths of response time (in seconds) for

a Use the sign test to determine whether sufficient evidence exists to indicate a difference in mean response for the two stimuli. Use a rejection region for which α ≤ .05.

b Test the hypothesis of no difference in mean response, using Student’s t test.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 15.3, Problem 6E

Chapter 15.3, Problem 8E

Chapter 15 Solutions

Mathematical Statistics with Applications

Ch. 15.3 - What significance levels between = .01 and = .15...Ch. 15.3 - Prob. 2E Ch. 15.3 - Clinical data concerning the effectiveness of two...Ch. 15.3 - Prob. 4E Ch. 15.3 - New food products are frequently subjected to...Ch. 15.3 - On clear, cold nights in the central Florida...Ch. 15.3 - A psychological experiment was conducted to...Ch. 15.3 - Refer to Exercise 12.15. Using the sign test, do...Ch. 15.3 - Prob. 9E Ch. 15.4 - The accompanying table gives the scores of a group...

Ch. 15.4 - Refer to Exercise 15.4. What answers are obtained...Ch. 15.4 - Refer to Exercise 15.6(a). Answer the question by...Ch. 15.4 - Eight subjects were asked to perform a simple...Ch. 15.4 - Two methods, A and B, for controlling traffic were...Ch. 15.4 - Dental researchers have developed a new material...Ch. 15.4 - Refer to Exercise 12.16. With = .01, use the...Ch. 15.4 - Suppose that Y1, Y2,, Yn is a random sample from a...Ch. 15.4 - The spokesperson for an organization supporting...Ch. 15.6 - Find the p-values associated with each of the...Ch. 15.6 - In some tests of healthy, elderly men, a new drug...Ch. 15.6 - Two plastics, each produced by a different...Ch. 15.6 - Prob. 24E Ch. 15.6 - Prob. 25E Ch. 15.6 - Prob. 26E Ch. 15.6 - Prob. 27E Ch. 15.6 - Prob. 28E Ch. 15.7 - The table that follows contains data on the leaf...Ch. 15.7 - Prob. 30E Ch. 15.7 - Three different brands of magnetron tubes (the key...Ch. 15.7 - An experiment was conducted to compare the length...Ch. 15.7 - Prob. 33E Ch. 15.7 - Prob. 34E Ch. 15.7 - Prob. 35E Ch. 15.8 - In a study of palatability of antibiotics for...Ch. 15.8 - Prob. 38E Ch. 15.8 - Prob. 39E Ch. 15.8 - A serious drought-related problem for farmers is...Ch. 15.8 - Prob. 41E Ch. 15.8 - Prob. 42E Ch. 15.8 - Prob. 43E Ch. 15.8 - Prob. 44E Ch. 15.8 - Prob. 45E Ch. 15.9 - Prob. 46E Ch. 15.9 - Prob. 47E Ch. 15.9 - Prob. 48E Ch. 15.9 - Prob. 49E Ch. 15.9 - Prob. 50E Ch. 15.9 - Prob. 52E Ch. 15.10 - Prob. 53E Ch. 15.10 - Prob. 54E Ch. 15.10 - Prob. 55E Ch. 15.10 - Prob. 56E Ch. 15.10 - Prob. 57E Ch. 15.10 - Prob. 58E Ch. 15.10 - Refer to Exercise 11.4. Regard both book and...Ch. 15.10 - Prob. 60E Ch. 15 - Prob. 62SE Ch. 15 - Prob. 63SE Ch. 15 - Prob. 64SE Ch. 15 - Prob. 65SE Ch. 15 - Prob. 67SE Ch. 15 - Prob. 69SE Ch. 15 - Prob. 70SE Ch. 15 - Prob. 71SE Ch. 15 - Prob. 72SE Ch. 15 - Prob. 74SE Ch. 15 - Prob. 75SE Ch. 15 - Prob. 76SE Ch. 15 - Prob. 77SE Ch. 15 - Prob. 78SE

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Solution Summary: The author concludes that there is no sufficient evidence to indicate a difference in mean response for the two stimuli.

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Chapter 15 Solutions