Answered: The National Institute of Standards and…

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

The National Institute of Standards and Technology (NIST) publishes procedures for inspecting the advertised contents of packaged goods.!° The discussion of these procedures includes an example of inspecting the weights of a sample of packages of ground beef from a particular grocer. An SRS of 12 packages are weighed (in pounds) according to the NIST procedures. The table shows each of the actual weichts along with the weight listed on the package label.

carry out the test to see if the mean difference in the measured weight minus the labels weight is less than 0

Table is available in the attached image.

The table below presents data comparing the labeled weight and the measured weight of samples:

| Sample | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---------------|------|------|------|------|------|------|------|------|------|------|------|------|
| Labeled weight| 1.85 | 1.21 | 1.56 | 1.98 | 1.07 | 1.55 | 1.02 | 1.44 | 1.33 | 2.03 | 1.73 | 1.16 |
| Measured weight| 1.67 | 1.14 | 1.48 | 1.84 | 0.84 | 1.39 | 1.00 | 1.19 | 1.17 | 1.83 | 1.59 | 1.05 |

This data provides a comparison between the weight indicated on the packaging (labeled weight) and the actual weight obtained through measurement (measured weight) for 12 samples.

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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