Specifications call for the wall thickness of two-liter polycarbonate bottles to

Question

Specifications call for the wall thickness of two-liter polycarbonate bottles to be 4 mils on average. (A mil is one thousandth of an inch.) A quality control engineer samples 15 two-liter polycarbonate bottles and measures the wall thickness in each bottle. They computed some descriptive statistics for the wall thickness. (a) Formulate a null hypothesis against an alternative hypothesis to verify that the wall thickness meets the specifications. (b) Interpret an error of type I in the context of this problem. (c) Interpret an error of type II in the context of this problem.

Explanation / Answer

a)

Ho: u = 4 mils
Ha: u =/= 4 mils [ANSWER]

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b)

A type I error is incorrectly rejecting a true null hypothesis.

Hence, a type I error is incorrectly saying that the two-liter polycarbonate bottles do not have a mean wall thickness of 4 mils, when in fact, the mean is 4 mils.

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c)

A type II error is incorrectly failing to reject a false null hypothesis.

Hence, a type II error is incorrectly saying that the two-liter polycarbonate bottles have a mean wall thickness of 4 mils, when in fact, the mean is not 4 mils.

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