In order to evaluate a spectrophotometric method for the determination of titanium concentration, the method was uased on 64 alloy samples containing different certified amounts of titanium. For each alloy, eight different concentrations of titanium were made. Additionally, two spectrophotometer machines were used in the lab to control for possible variation between machines. Each machine received a random allocation of each concentration of alloy. Below you will find an ANOVA analysis for difference in certified mean concentrations detected using machines as a blocking fator. (You will have to calculate some of the values in the tables marked with ). Concentration 1.93 Machine 0.16 Residuals 14.27 Which one of the following is correct given the ANOVA table (using a 5% level of significance)? A. The method was able to detect the difference in the concentrations of titanium alloys; additionally, there was a detectable difference in the mean concentration between machines. B. The method was able to detect the difference in the concentrations of titanium alloys; additionally, there was no detectable difference in the mean concentration between machines. C. The method was not able to detect the difference in the concentrations of titanium alloys; additionally, there was a detectable difference in the mean concentration between machines. D. The method was not able to detect the difference in the concentrations of titanium alloys; additionally, there was no detectable difference in the mean concentration between machines.

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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In order to evaluate a spectrophotometric method for the determination of titanium concentration, the method was uased on 64 alloy samples containing different certified amounts of titanium. For each alloy, eight different concentrations of titanium were made. Additionally, two spectrophotometer machines were used in the lab to control for possible variation between machines. Each machine received a random allocation of each concentration of alloy. Below you will find an ANOVA analysis for difference in certified mean concentrations detected using machines as a blocking fator. (You will have to calculate some of the values in the tables marked with ).

Concentration 1.93

Machine 0.16

Residuals 14.27

Which one of the following is correct given the ANOVA table (using a 5% level of significance)?

A. The method was able to detect the difference in the concentrations of titanium alloys; additionally, there was a detectable difference in the mean concentration between machines.
B. The method was able to detect the difference in the concentrations of titanium alloys; additionally, there was no detectable difference in the mean concentration between machines.
C. The method was not able to detect the difference in the concentrations of titanium alloys; additionally, there was a detectable difference in the mean concentration between machines.
D. The method was not able to detect the difference in the concentrations of titanium alloys; additionally, there was no detectable difference in the mean concentration between machines.

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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