Answered: bottled water company bottles varying…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter29: Tolerance, Clearance, And Interference

Section: Chapter Questions

Problem 16A: Spacers are manufactured to the mean dimension and tolerance shown in Figure 29-12. An inspector...

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A bottled water company bottles varying sizes of water, from 8-ounce to 1-gallon containers. The company has determined that the mean quantity in their 20-ounce bottles is 20.8 ounces with a standard deviation of 0.6 ounces. The bottling plant manager believes his machines are overfilling the bottles. A random sample of 30 bottles is taken, and the mean number of ounces of water is determined to be 20.9. Under the assumption that the true mean ounces of water is 20.8, 100 simulated means for samples of size 30 are shown in the dotplot.

Using the dotplot, is there evidence that machines are overfilling the 20-ounce bottles?

A.) Yes, since a sample mean of 20.9 is greater than the mean, 20.8, there is evidence that the true mean ounces of water is greater than 20.8.

B.) Yes, since a sample mean of 20.9 never occurred in the 100 simulated values, there is evidence that the true mean ounces of water is greater than 20.8.

C.) No, since a sample mean of 20.9 or more occurred 19 out of 100 times, there is insufficient evidence that the true mean ounces of the bottles of water is greater than 20.8.

D.) No, since a sample mean of 20.9 never occurred in the dotplot, it is not possible that a random sample of 30 bottles will have a mean number of ounces of 20.9. Therefore, there is insufficient evidence that the true mean ounces is greater than 20.8.

Mean Ounces of Water for 20-ounce Bottles
20.50
20.60
20.70
20.80
20.90
21.00
21.10
Simulated means of samples, n = 30
0000

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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