4th Edition

ISBN: 9780321826275

Author: Richard D. De Veaux

Publisher: PEARSON

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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 19, Problem 32E

Alzheimer’s Testing for Alzheimer’s disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. A group of researchers (Solomon et al., 1998) devised a 7-minute test to serve as a quick screen for the disease for use in the general population of senior citizens. A patient who tested positive would then go through the more expensive battery of tests and medical diagnosis. The authors reported a false-positive rate of 4% and a false-negative rate of 8%.

a) Put this in the context of a hypothesis test. What are the null and alternative hypotheses?
b) What would a Type I error mean?
c) What would a Type II error mean?
d) Which is worse here, a Type I or Type II error? Explain.
e) What is the power of this 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 19, Problem 31E

Chapter 19, Problem 33E

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Chapter 19 Solutions

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Ch. 19 - Prob. 5E Ch. 19 - Prob. 6E Ch. 19 - Prob. 7E Ch. 19 - Prob. 8E Ch. 19 - Prob. 9E Ch. 19 - More critical values For each of the following...Ch. 19 - SECTION 16.4 11. Errors For each of the following...Ch. 19 - More errors For each of the following situations,...Ch. 19 - Prob. 13E Ch. 19 - 14. Which alternative? In each of the following...Ch. 19 - CHAPTER EXERCISES 13. P-value A medical researcher...Ch. 19 - Prob. 16E Ch. 19 - Alpha A researcher developing scanners to search...Ch. 19 - Prob. 18E Ch. 19 - Prob. 19E Ch. 19 - Significant again? A new reading program may...Ch. 19 - Prob. 21E Ch. 19 - Is the Euro fair? Soon after the Euro was...Ch. 19 - 23. Approval 2011 In November 2011, Barack Obama’s...Ch. 19 - Prob. 24E Ch. 19 - Prob. 25E Ch. 19 - Prob. 26E Ch. 19 - Prob. 27E Ch. 19 - Prob. 28E Ch. 19 - Prob. 29E Ch. 19 - Prob. 30E Ch. 19 - 31. Homeowners 2009 In 2009, the U.S. Census...Ch. 19 - Alzheimers Testing for Alzheimers disease can be a...Ch. 19 - Prob. 33E Ch. 19 - Quality control Production managers on an assembly...Ch. 19 - Prob. 35E Ch. 19 - 36. Production Consider again the task of the...Ch. 19 - Equal opportunity? A company is sued for job...Ch. 19 - Stop signs Highway safety engineers test new road...Ch. 19 - Prob. 39E Ch. 19 - Ads A company is willing to renew its advertising...Ch. 19 - 41. Software, part II 203 students signed up for...Ch. 19 - Prob. 42E Ch. 19 - Prob. 43E Ch. 19 - Catheters During an angiogram, heart problems can...Ch. 19 - Prob. 45E Ch. 19 - Prob. 46E Ch. 19 - Prob. 47E Ch. 19 - Faulty or not? You are in charge of shipping...Ch. 19 - Prob. 49E Ch. 19 - Prob. 50E

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Solution Summary: The author explains the meaning of type-I error, which is false positive, when the alternative hypothesis is true.

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