13th Edition

ISBN: 9780134462455

Author: Mario F. Triola

Publisher: PEARSON

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Chapter 9.2, Problem 27BB

No Variation in a Sample An experiment was conducted to test the effects of alcohol. Re-searchers measured the breath alcohol levels for a treatment group of people who drank ethanol and another group given a placebo. The results are given below (based on data from “Effects of Alcohol Intoxication on Risk Taking, Strategy, and Error Rate in Visuomotor Performance,” by Streufert et al.. Journal of Applied Psychology, Vol. 77, No. 4). Use a 0.05 significance level to test the claim that the two sample groups come from populations with the same mean.

Treatment Group: n₁ = 22, x ¯ 1 = 0.049, s₁ = 0.015

Placebo Group: n₂ = 22, x ¯ 2 = 0.000, s₂ = 0.000

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 9.2, Problem 26BB

Chapter 9.3, Problem 1BSC

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Solution Summary: The author concludes that there is sufficient evidence to reject the claims that the two sample groups come from populations with the same mean.

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