Answered: a. What is the shape of the sampling…

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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Is it more expensive to live in California or Florida? Monthly cost of living expenses for California are approximately Normal with mean μC=$10,800��=$10,800 and standard deviation σC=$3,200��=$3,200. Monthly cost of living expenses for Florida are approximately Normal with mean μF=$8,500��=$8,500 and standard deviation σF=$2,700.��=$2,700. Suppose we select independent SRSs of 16 residents of California and 9 residents of Florida and calculate the sample mean monthly cost of living, x¯C�¯� and x¯F�¯�. a. What is the shape of the sampling distribution of x¯C−x¯F?�¯�−�¯�? Why? b. Find the mean and standard deviation of the sampling distribution of x¯C−x¯F�¯�−�¯�. c. Calculate the probability that the average monthly cost of living expense of the 16 randomly selected California residents is less than the average monthly cost of living expense of the 9 randomly selected Florida residents.

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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