Understandable Statistics: Concepts and Methods

12th Edition

ISBN: 9781337119917

Author: Charles Henry Brase, Corrinne Pellillo Brase

Publisher: Cengage Learning

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Textbook Question

Chapter 8.5, Problem 1P

Statistical Literacy Consider a hypothesis test of difference of means for two independent populations x₁ and x₂.

(a) What does the null hypothesis say about the relationship between the two population means?
(b) If the sample test statistic has a z distribution, give the formula for z.
(c) If the sample test statistic has a t distribution, give the formula for t.

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 8.4, Problem 24P

Chapter 8.5, Problem 2P

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Chapter 8 Solutions

Understandable Statistics: Concepts and Methods

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Solution Summary: The author explains the null hypothesis, which is related to population parameter, and the formula z sample test statistic.

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