Intro Stats, Books a la Carte Edition (5th Edition)

5th Edition

ISBN: 9780134210285

Author: Richard D. De Veaux, Paul Velleman, David E. Bock

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 16, Problem 11E

SECTION 16.4

11. Errors For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain briefly.

a) A bank wants to know if the enrollment on their website is above 30% based on a small sample of customers. They test H₀: p = 0.3 vs. H_A: p > 0.3 and reject the null hypothesis. Later they find out that actually 28% of all customers enrolled.
b) A student tests 100 students to determine whether other students on her campus prefer Coke or Pepsi and finds no evidence that preference for Coke is not 0.5. Later, a marketing company tests all students on campus and finds no difference.
c) A human resource analyst wants to know if the applicants this year score, on average, higher on their placement exam than the 52.5 points the candidates averaged last year. She samples 50 recent tests and finds the average to be 54.1 points. She fails to reject the null hypothesis that the mean is 52.5 points. At the end of the year, they find that the candidates this year had a mean of 55.3 points.
d) A pharmaceutical company tests whether a drug lifts the headache relief rate from the 25% achieved by the placebo. They fail to reject the null hypothesis because the P-value is 0.465. Further testing shows that the drug actually relieves headaches in 38% of people.

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 16, Problem 10E

Chapter 16, Problem 12E

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Chapter 16 Solutions

Intro Stats, Books a la Carte Edition (5th Edition)

Ch. 16.2 - An experiment to test the fairness of a roulette...Ch. 16.2 - Prob. 2JC Ch. 16.2 - Prob. 3JC Ch. 16.3 - Prob. 4JC Ch. 16.3 - Prob. 5JC Ch. 16.3 - Prob. 6JC Ch. 16.3 - Prob. 7JC Ch. 16.4 - Remember the bank thats sending out DVDs to try to...Ch. 16.4 - Prob. 9JC Ch. 16.4 - For the bank, which situation has higher power: a...

Ch. 16 - True or false Which of the following are true? If...Ch. 16 - False or true Which of the following are true? If...Ch. 16 - P-values Which of the following are true? If...Ch. 16 - Prob. 4E Ch. 16 - Prob. 5E Ch. 16 - Prob. 6E Ch. 16 - Prob. 7E Ch. 16 - More critical values For each of the following...Ch. 16 - Prob. 9E Ch. 16 - Significant again? A new reading program may...Ch. 16 - SECTION 16.4 11. Errors For each of the following...Ch. 16 - More errors For each of the following situations,...Ch. 16 - CHAPTER EXERCISES 13. P-value A medical researcher...Ch. 16 - Prob. 14E Ch. 16 - Alpha A researcher developing scanners to search...Ch. 16 - Prob. 16E Ch. 16 - Prob. 17E Ch. 16 - Is the Euro fair? Soon after the Euro was...Ch. 16 - Prob. 19E Ch. 16 - Prob. 20E Ch. 16 - Prob. 21E Ch. 16 - Prob. 22E Ch. 16 - Prob. 23E Ch. 16 - Prob. 24E Ch. 16 - Prob. 25E Ch. 16 - Prob. 26E Ch. 16 - Prob. 27E Ch. 16 - Alzheimers Testing for Alzheimers disease can be a...Ch. 16 - Prob. 29E Ch. 16 - Quality control Production managers on an assembly...Ch. 16 - Cars, again As in Exercise 29, state regulators...Ch. 16 - Prob. 32E Ch. 16 - Equal opportunity? A company is sued for job...Ch. 16 - Stop signs Highway safety engineers test new road...Ch. 16 - Prob. 35E Ch. 16 - Ads A company is willing to renew its advertising...Ch. 16 - Prob. 37E Ch. 16 - Prob. 38E Ch. 16 - Prob. 39E Ch. 16 - Catheters During an angiogram, heart problems can...Ch. 16 - Prob. 41E Ch. 16 - Prob. 42E Ch. 16 - Prob. 43E Ch. 16 - Faulty or not? You are in charge of shipping...Ch. 16 - Prob. 45E Ch. 16 - Prob. 46E Ch. 16 - Prob. 47E Ch. 16 - Prob. 48E

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Solution Summary: The author explains the two types of errors: the null hypothesis and the type-I error.

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