Consider a manufacturing process that is producing hypodermic needles that will
ID: 3272896 • Letter: C
Question
Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need to have a diameter of 1.65 mm—too big and they would hurt the donor (even more than usual), too small and they would rupture the red blood cells, rendering the donated blood useless. Thus, the manufacturing process would have to be closely monitored to detect any significant departures from the desired diameter. During every shift, quality control personnel take a sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected.
1) Define the parameter of interest in the context of this study and assign an appropriate symbol to it.
The average needle diameter of the sample taken (p-hat).
The true, long-run average needle diameter ().
The average needle diameter of the sample taken (x-bar).
The true, long-run average needle diameter ().
2) State the appropriate null and alternative hypotheses using the symbol defined in (a).
Null: ( = 1.65mm);Alt: ( 1.65mm).
Null: ( 1.65mm);Alt: ( = 1.65mm).
3) Describe what a Type I error would be in this study.
Average diameter is 1.65 mm, and we don't find strong evidence that it is different than 1.65. mm
Average diameter is not 1.65 mm, and we don't find strong evidence that it is different than 1.65 mm.
Average diameter is 1.65 mm, but we decide that it is not 1.65 mm.
Average diameter is 1.65 mm, and we decide that it is not 1.65 mm.
Describe what a Type II error would be in this study.
Average diameter is 1.65 mm, and we don't find strong evidence that it is different than 1.65 mm.
Average diameter is not 1.65 mm, but we don't find strong evidence that it is different than 1.65 mm.
Average diameter is not 1.65 mm, and we decide that it is not 1.65 mm.
Average diameter is 1.65 mm, but we decide that it is not 1.65 mm.
Explanation / Answer
Solution1:
From the line: every shift, quality control personnel take a sample of several needles and measure their diameters
we measure sample means which represent true population
Parameter :true mean
The true, long-run average needle diameter ().
Solution2:
Null: ( = 1.65mm);
Alt: ( 1.65mm).
Solution3:
What are type I and type II errors, and how we distinguish between them? Briefly:
type1:
mean=1.65
mean not =1.65
Average diameter is 1.65 mm, and we don't find strong evidence that it is different than 1.65. mm
Type2:
Average diameter is not 1.65 mm, but we don't find strong evidence that it is different than 1.65 mm.
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