Answered: A 95% confidence interval for the mean…

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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A 95% confidence interval for the mean body mass index (BMI) of young American women is 26.8±0.626.8±0.6.

One of your classmates interprets this interval in the following way: “The mean BMI of young American women cannot be 28.”

Is your classmate’s interpretation correct? If not, what is the correct interpretation of the confidence interval?

Incorrect. We are 95% confident that future samples of young women will have mean BMI between 26.2 and 27.4.

Incorrect. We are 95% confident that the interval from 26.2 and 27.4 captures the BMI of all young American women.

Correct. The interval states that the mean BMI of young American women is between 26.2 and 27.4, so the mean cannot be 28.

Incorrect. We are 95% confident that the interval from 26.2 and 27.4 captures the true mean BMI of all young American women.

Incorrect. If we take many samples, the population mean BMI will be between 26.2 and 27.4 in about 95% of those samples.

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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A $(1 - α) %$ for the population mean tells us that we are $(1 - α) %$ confident that the confidence interval will capture the true mean.

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