Answered: An article presents measurements of…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

An article presents measurements of total solids, in g/L, for seven sludge specimens. The results are 19, 6, 26, 43, 25, 20, and 32. Assume the distribution of total solids is approximately symmetric.

a) Can you conclude that the mean concentration of total solids is greater than 14 g/L? Compute the appropriate test statistic and find the P-value.

b) Can you conclude that the mean concentration of total solids is less than 30 g/L? Compute the appropriate test statistic and find the P-value.

c) An environmental engineer claims that the mean concentration of total solids is equal to 18 g/L. Can you conclude that the claim is false? Compute the appropriate test statistic and find the P-value.

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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