SOLUTION: An assembly line is supposed to produce defective widgets at a rate of 1 every 75 produced. a) Suppose a quality control engineer takes a random sample of 10 widgets from the asse

Question 535259: An assembly line is supposed to produce defective widgets at a rate of 1 every 75 produced.
a) Suppose a quality control engineer takes a random sample of 10 widgets from the assembly line. If the line is working properly, what are the chances of the engineer finding at most two defective widgets in the sample?
b) Over the course of a week the engineer collects an SRS of 1000 widgets from the line. What is the approximate sampling distribution of the proportion of defective widgets in the sample?
c) In the sample from part b, the engineer finds 17 defective widgets. Is this evidence at th 5% level that the line is not working properly? (i.e. producing defective at a higher rate then it should be?)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An assembly line is supposed to produce defective widgets at a rate of 1 every 75 produced.
a) Suppose a quality control engineer takes a random sample of 10 widgets from the assembly line. If the line is working properly, what are the chances of the engineer finding at most two defective widgets in the sample?
Binomial Problem with n = 10 and p(defect) = 1/75
P(0<= x <=2) = binomcdf(10,1/75,2) = 0.9997
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b) Over the course of a week the engineer collects an SRS of 1000 widgets from the line. What is the approximate sampling distribution of the proportion of defective widgets in the sample?
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mean = np = 1000*(1/75) = 13 1/3
std = sqrt(npq) = sqrt(13.333*(74/75)) = 3.627
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c) In the sample from part b, the engineer finds 17 defective widgets. Is this evidence at the 5% level that the line is not working properly? (i.e. producing defective at a higher
Ho: u <= 13 1/3
Ha: u > 13 1/3 (claim)
z(17) = (17-13.33333)/3.627 = 1.0109
p-value = P(z > 1.0109) = 0.1560
Since the p-value is greater than 5%, fail to reject Ho.
The test results do not support the claim.
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Cheers,
Stan H.
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