Answered: Hello, Let me start by mentioning that…

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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Hello,

Let me start by mentioning that my question is not about the t-test, but rather CIs for the mean. I'm familiar with interpreting the t-test.

When calculating confidence intervals for the mean, we find a t-value. Let's say we find a t-value of 44 when comparing the sample mean and sample standard deviation of 56.7 and 0.37, respectively. The population mean is 54.5 for the scenario.

How would we interpret the t-value in general terms?

I understand the t-test is comparing means, but I'm not sure that the t-value in the context of the CI would be interpreted the same. I also understand how to interpret the scenario in terms of the CI. It is the t-value specifically here that I'm trying to interpret correctly (although not part of the assignment).

Thank you.

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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