Answered: A demographics researcher claims that…

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

A demographics researcher claims that the mean household income in a recent year is the same in Ada County, Idaho, and Cameron Parish, Louisiana. In Ada County, a sample of 18 residents has a mean household income of $58,300 and a standard deviation of $9,000. In Cameron Parish, a sample of 20 residents has a mean household income of $56,600 and a standard deviation of $15,600. At α=0.10, can you reject the demographics researcher’s claim. Assume the population variances are not equal.

a) Null and Alternative Hypothesis

b) Determine the critical value using the t-table

c) Determine the rejection region

d) Calculate test statistic

e) Accept or reject the null hypothesis

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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