Answered: Analyses of drinking water samples for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Analyses of drinking water samples for 100 homes in each of two different sections of a city gave the following information on lead levels (in parts per million).

sample size: 100 (section 1), 100 (section 2)

mean: 34.1 (section 1), 3.58 (section 2)

standard deviation: 6.0 (section 1), 6.1 (section 2)

a) Calculate the test statistic and its p-value to test for a difference in the two population means. (Use Section 1 − Section 2. Round your test statistic to two decimal places and your p-value to four decimal places.)

b) Calculate a 95% confidence interval to estimate the difference in the mean lead levels in parts per million for the two sections of the city. (Use Section 1 − Section 2. Round your answers to two decimal places.)

______ parts per million to _____ parts per million

c) Suppose that the city environmental engineers will be concerned only if they detect a difference of more than 5 parts per million in the two sections of the city. Based on your confidence interval in part (b), is the statistical significance in part (a) of practical significance to the city engineers? Explain.

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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