12th Edition

ISBN: 9780321836960

Author: Mario F. Triola

Publisher: PEARSON

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Chapter 8, Problem 6RE

Monitoring Lead in Air Listed below are measured amounts of lead (in micrograms per cubic meter, or μg/m³, in the air. The Environmental Protection Agency has established an air quality standard for lead of 1.5 μg/m³. The measurements shown below constitute a simple random sample of measurements recorded at Building 5 of the World Trade Center site on different days immediately following the destruction caused by the terrorist attacks of September 11, 2001. After the collapse of the two World Trade Center buildings, there was considerable concern about the quality of the air. Use a 0.05 significance level to test the claim that the sample is from a population with a mean greater than the EPA standard of 1.5 μg/m³.

5.40 1.10 0.42 0.73 0.48 1.10

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, Problem 5RE

Chapter 8, Problem 7RE

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Solution Summary: The author concludes that there is no sufficient evidence to support the claim that the sample is from a population with mean greater than the EPA standard of 1.5 g/m 3.

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