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# Level of Significance

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A flour manufacturer packs flour into paper bags, each of which is supposed to hold 10 pounds, or 160 ounces. Some customers have complained that the bags hold only 9.5 pounds, or 152 ounces. A test is conducted to determine whether the complaint is warranted. The weight of each bag is normally distributed with a Population Standard Deviation of 5 ounces. A sample of 16 bags yields a mean weight of 156 ounces. Shall we reject the null hypothesis of Mean Weight is exactly equal to 160 ounces with a level of significance of .05? Set up the Hypothesis test in "standard form" and then carry out the test.

##### Solution Summary

A flour manufacturer packs flour into paper bags, each of which is supposed to hold 10 pounds, or 160 ounces. Some customers have complained that the bags hold only 9.5 pounds, or 152 ounces. A test is conducted to determine whether the complaint is warranted. The weight of each bag is normally distributed with a Population Standard Deviation of 5 ounces. A sample of 16 bags yields a mean weight of 156 ounces. Shall we reject the null hypothesis of Mean Weight is exactly equal to 160 ounces with a level of significance of .05? Set up the Hypothesis test in "standard form" and then carry out the test.

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This is a mean confidence interval question:
H0: m=160 vs. H1: m<>160
We will construct the 95% confidence interval of the sample mean M=156. If 160 ounces falls within the interval, we can accept H0; if not, we reject it.
When Population Standard Deviation s is known to be 5, then we apply the formula: ...

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