Answered: What is the meaning of a confidence…

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

What is the meaning of a confidence interval? Your answer should clearly distinguish
between the sample mean and population mean (also referred to as the “true” mean.) What is the 95%
confidence interval for a set of 5 replicate measurements with a mean of 120.25 and a standard
deviation of 13.12? How can the confidence interval be improved?

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 + ...

Expert Solution

Step 1

For the provided information the followings are inferred.

For the considered set of 5 replicate measurements (i.e., the sample size, $n = 5$ ), the stated mean (i.e., the sample mean, $\bar{x}$ ) and standard deviation (i.e., the sample standard deviation, $s$ ) are 120.25 and 13.21 respectively. With usual denotations, it is represented as: $\bar{x} = 120.25$ and $s = 13.12$ .