Answered: The processing of raw coal involves…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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The processing of raw coal involves “washing,” in which coal ash (nonorganic, incombustible material) is removed. The article “Quantifying Sampling Precision for Coal Ash Using Gy’s Discrete Model of the Fundamental Error” (Journal of Coal Quality, 1989:33–39) provides data relating the percentage of ash to the volume of a coal particle.

The average percentage of ash for six volumes of coal particles was measured. The data are as follows:

Volume (cm³)	0.01	0.06	0.58	2.24	15.55	276.02
Percent ash	3.32	4.05	5.69	7.06	8.17	9.36

Using the most appropriate model, construct a 95% confidence interval for the mean percent ash for particles with a volume of 50 cm³. Round the answers to three decimal places.

The 95% confidence interval is , .

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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