Answered: 5. A company that manufactures steel…

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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5. A company that manufactures steel wires
guarantees that the mean breaking strength (in
kilonewtons) of the wires is greater than 50. They
measure the strengths for a sample of wires and
test H0: µ = 50 versus H1: µ > 50
a. If a Type I error is made, what conclusion will be
drawn regarding the mean breaking strength?
b. If a Type II error is made, what conclusion will be
drawn regarding the mean breaking strength?
6. Data from the National Association of Realtors
indicates that the mean price of a home in
Denver, from April through June of 2012 was
260.7 thousand dollars. A random sample of 50
homes sold in 2013 had a mean price of 290.5
thousand dollars.
a. Assume the population standard deviation is
σ=$150,000. Can you conclude that the mean
price in 2013 differs from the mean price in April
through June of 2012? Use a 5% significance
level.
b. Following is a boxplot of the data. Explain why it
is unreasonable to assume that the population is
approximately normally distributed.
c. Explain why the assumptions for the hypothesis
test are satisfied even though the population is not
normal.

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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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