8.5 Suppose you have a batch of 30 items to be inspected to determine, in each case, whether the item meets established quality standards or is defective. In the process of determining whether an item...

8.5

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Use the hypothesis H₀: p<= 0.1="" vs="">_a: P>0.1

Extracted text: 8.5 Suppose you have a batch of 30 items to be inspected to determine, in each case, whether the item meets established quality standards or is defective. In the process of determining whether an item is acceptable (A) or defective (D), it is destroyed, so sampling is necessarily without replacement. The articles have been produced with a machine that has been decided to discard if it produces more than 10% defective a)State the relevant set of hypotheses, either in terms of the number of defectives (D) or the ratio D/30 b)Find the decision rule for a test with a = 0.0394, with a sample size n = 4. c) Find the decision rule for a test with a = 0.001 with n = 4. d) Calculate the probabilities of Type II Error for D= 4(p= 0.133), D = 6(p = 0.2), D = 8(p= 0.267), D(10(p=0.333) ,D= 14(p=0.467), D = 18(p = 0.6)y D = 20(p = 0.667) part b) and for part c) e) In quality control problems like this, it is customary to work with the "operating characteristic function", which is defined as 1-power function. Graph the character- istic functions of the tests in b) and c) and compare them