Answered: The admissions director for a…

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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The admissions director for a university found that (107.8, 116.2) is a 95% confidence interval for the mean IQ score of all freshmen.

Is the following explanation correct, based on that information?

There is a 95% probability that the interval from 107.8 to 116.2 contains ?¯x¯.

Incorrect. The point estimate ?¯x¯ will always be in the center of the confidence interval, so there is a 100% chance that ?¯x¯ will be in the interval.

Incorrect. If we take many samples, about 95% of them will contain the interval (107.8, 116.2)

Incorrect. It should say that there is a 95% probability that the interval from 107.8 to 116.2 contains ?μ.

Incorrect. 95% of the students at this university have an IQ between 107.8 and 116.2.

Correct. That is the meaning of 95% confidence.

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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