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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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PLEASE ANSWER ALL THE PARTS OF THE QUESTION (THIS IS NOT A GRADED ASSIGNMENT)

1. Suppose the distribution of cholesterol levels in a population of men is approximately normally distributed with a mean of 200 mg/dL and a standard deviation of 32 mg/dL.

A. What is the standard deviation of the sampling distribution of ˉxˉ for n=25? Write your answer as a decimal value rounded to four decimal places.

B. What condition allows us to say that the value in part (A) is approximately true?

C. What is the shape of the sampling distribution of ˉxˉ for n=25?

D. What condition allows us to answer as we did in part (C)?

E. You take a random sample of 25 males from this population and find the average level of the sample to be 188 mg/dL. How unusual is this sample? Show your work (conditions, mechanics, and context)

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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