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Name: The meat-packing department of a large grocery store packs ground beef
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Description: The meat-packing department of a large grocery store packs ground beef in two-pound portions. Supervisors are concerned that their machine is no longer packaging the beef to the required specifications. To test the claim that the mean weight of groun

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 meat-packing department of a large grocery store packs ground beef in two-pound portions. Supervisors are concerned that their machine is no longer packaging the beef to the required specifications. To test the claim that the mean weight of ground beef portions is not 2.00 pounds, the
supervisors calculate the mean weight for a simple random sample of 20 packages of beef. The sample mean is 2.10 pounds with a standard deviation of 0.33 pounds.

Is there sufficient evidence at the 0.01 level of significance to show that the machine is not working properly? (Assume that the weights are normally distributed.)

Use the Critical Value Method. Clearly show all steps.

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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