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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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professor Thomas Stanley of Georgia state university has surveyed millionaires since 1973. Among other information, professor Stanley obtains estimates for the mean age of all US millionaires. Suppose that one year's study involved a simple random sample of 36 US millionaires whose main age was 58.53 years with a sample standard deviation of 13.36 years.

a) calculate a 95% CI for the mean age of US millionaires that year. interpret

b) calculate a 95% prediction interval for the mean age of a randomly selected US millionaire that year. assume the population was is normally distributed. interpret

c) calculate a 99% CI for the standard deviation of the age of US millionaires that year

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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