Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

4th Edition

ISBN: 9780134686974

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

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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 4.4, Problem 136AYU

The Marriage Problem There is an infamous problem from mathematics that attempts to quantify the number of potential mates one should date before choosing one’s “true love.” The function

L ( x ) = − x ln x

represents the probability of finding the ideal mate after rejecting the first x proportion of potential mates. For example, if you reject the first 20 % = 0.20 of individuals you date, the probability of finding the ideal mate to be greater than 0.332 and you are only willing to date up to 20 individuals, you should reject the first 0.2 ( 20 ) = 4 individuals before attempting to decide on the ideal mate. Presumably, you are using those first 4 individuals to help you decide which traits you value in a mate.

Determine and interpret L ( 0.1 ) .

Determine and interpret L ( 0.6 ) .

What is the domain of L ?

Graph L = L ( x ) over the domain.

Judging on the basis of the approach suggested by the model, what is the value of x that maximizes L ? What is the highest probability of finding the ideal mate?

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Chapter 4.4, Problem 135AYU

Chapter 4.4, Problem 137AYU

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Weber's law, a concept taught in most Introduction to Psychology courses, states that the ratio of the intensity of a stimulus to the "just noticeable" increment in intensity is constant, that is, the ratio doesn't depend on the intensity of the stimulus. The ratio is called the "Weber fraction," so a concise statement of Weber's law is that "the Weber fraction is constant, regardless of the stimulus intensity." It turns out that Weber's law is not so much a law as it is a rule of thumb, since it is violated in many situations. For instance, for some auditory stimuli, the Weber fraction does depend systematically on the stimulus intensity. The following bivariate data are the experimental data obtained for one listener in an auditory intensity discrimination task. For each of the ten stimulus intensities x (in decibels), the experimental Weber fraction y (in decibels) is shown. For these data, the least-squares regression line is =y−2.84860.0900x . This line is shown in the…

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Chapter 4 Solutions

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

Ch. 4.1 - Find f( 3 ) if f( x )=4 x 2 +5x . (pp. 60-62)Ch. 4.1 - Find f(3x) if f(x)=42 x 2 . (pp. 60-62)Ch. 4.1 - Find the domain of the function f(x)= x 2 1 x 2 25...Ch. 4.1 - 4. Given two functions f and g, the ___________,...Ch. 4.1 - True or False If f(x)= x 2 and g(x)= x+9 , then...Ch. 4.1 - 6. If and , which of the following does (fg) (x)...Ch. 4.1 - 7. If H=fg and , which of the following cannot be...Ch. 4.1 - 8. True or False The domain of the composite...Ch. 4.1 - 9. In Problems 9 and 10, evaluate each expression...Ch. 4.1 - In Problems 9 and 10, evaluate each expression...

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Solution Summary: The author calculates the probability of finding the ideal mate after rejecting the first x proportions of potential mates.

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