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recannon02
recannon02
10.03.2021 • 
Mathematics

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. A dotplot titled Mean ounces of water for 20-ounce bottle. A number line labeled stimulated means of samples, n = 30, goes from 20.50 to 21.10. 20.53, 1; 20.55, 1; 20.56, 2; 20.61, 4; 20.63, 1; 20.64, 2; 20.67, 1; 20.68, 1; 20.69, 3; 20.70, 3; 20.71, 2; 20.72, 2; 20.73, 2; 20.74, 5; 20.75, 2; 20.76, 3; 20.77, 1; 20.78, 7; 20.79, 4; 20.80, 6; 20.81, 6; 20.82, 4; 20.83, 6; 20.87, 1; 20.88, 1; 20.91, 5; 20.92, 2; 20.93, 1; 20.94, 4; 20.95, 3; 20.96, 2.

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

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.
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.
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.
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.

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