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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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Question

The Economic Policy Institute periodically issues reports on wages of entry level workers. The institute reported that extry level wages for male college graduates were $21.68 per hour and for female college graduates were $18.80 per hour in 2011. Assume the standard deviation for male graduates is $2.30, and for female graduates it is $2.05.

Part a) What is the probability that a simple of 50 male graduates will provide a sample mean within $0.50 of the population mean, $21.68?

Part b) What is the probability that a simple 50 female graduates will provide a sample mean within $0.50 of the population mean, $18.80?

Part c) In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a sample estimate within $0.50 of the population mean? Why?

Part d) What is the probability that a simple random sample of 120 female graduates will provide a sample mean more than $0.30 below the population mean?

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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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