The fun size of a Snickers bar is supposed to weigh 20 grams. Because the penalty for selling candy bars under their advertised weight is severe, the manufacturer calibrates the machine so the mean weight is 20.1 grams. The quality-control engineer at MMMars, the Snickers manufacturer, is concerned about the calibration. He obtains a random sample of 10 candy bars, weighs them, and obtains the data shown in Table. Should the machine be shut down and calibrated? Because shutting down the plant is very expensive, he decides to conduct the test at the α = 0.01 level of significance.Weight: 19.619.920.521.520.620.620.319.719.5

Given data: 19.6,19.9,20.5,21.5,20.6,20.6,20.3,19.7,19.5 n = 9

Answered: The fun size of a Snickers bar is…

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 fun size of a Snickers bar is supposed to weigh 20 grams. Because the penalty for selling candy bars under their advertised weight is severe, the manufacturer calibrates the machine so the mean weight is 20.1 grams. The quality-control engineer at MMMars, the Snickers manufacturer, is concerned about the calibration. He obtains a random sample of 10 candy bars, weighs them, and obtains the data shown in Table. Should the machine be shut down and calibrated? Because shutting down the plant is very expensive, he decides to conduct the test at the α = 0.01 level of significance.

Weight:

19.6

19.9

20.5

21.5

20.6

20.3

19.7

19.5

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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