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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

A personnel director in a particular state claims that the mean annual income is greater in one of the state's counties (county A) than it is in another county (county B). In County A, a random sample of 6 residents has a mean annual income of $41,500 and a standard deviation of $8500. In County B, a random sample of 8 residents has a mean annual income of $37,600 and a standard deviation of $5900. At α=0.10, answer parts (a) through (e). Assume the population variances are not equal.

Identify the claim and state H0 and Ha.
What are
H0
and
Ha?
Find the critical value(s) and identify the rejection region(s).
Select the correct rejection region(s) below.
Find the standardized test statistic.
Decide whether to reject or fail to reject the null hypothesis.
Interpret the decision in the context of the original claim.

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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