Answered: A metallurgist makes several…

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 metallurgist makes several measurements of the melting temperature of a certain alloy
and computes a 95% confidence interval to be 2038±2°C. Assume the measuring process
for temperature is unbiased. True or false:
a) There is 95% probability that the true melting temperature is in the interval 2038 ±
2°C.
b) If the experiment were repeated, the probability is 95% that the mean measurement
from that experiment would be in the interval 2038 ± 2°C.
c) If the experiment were repeated, and a 95% confidence interval computed, there is
95% probability that the confidence interval would cover the true melting point.
d) If one more measurement were made, the probability is 95% that it would be in the
interval 2038 ± 2°C.

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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