Answered: The manager of a department store…

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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The manager of a department store considers establishing a new billing system for
the store’s credit customers. After a thorough analysis, she determines that the new
system will be cost effective only if the mean monthly account is more than $170.
A sample of 400 monthly accounts is drawn, for which the sample mean is $178. The
manager knows that the accounts are approximately normally distributed with a
standard deviation of $65.
1) Can the managers conclude that the new system will be cost effective with a 5%
significance level? Explain in detail your answer.
2) What is the smallest significance level at which the manager can reject the
statement that the new system is not cost-effective? Explain in detail your answer

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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