Question 1206623: A computer company checks every computer it produces before shipping. Each computer undergoes a series of 100 tests. The number of tests it fails will be used to determine whether the computer is Good or Defective. If it fails more than a certain number, it will be classified as Defective and will not be shipped. From past history, the distribution of the number of tests failed is known for both Good and Defective computers. The probabilities associated with each outcome are listed in the table below:
NUMBER OF TEST FAILED 0 1 2 3 4 5MORETHAN5
GOOD % 80 12 2 3 2 1 0
DEFECTIVE% 0 10 70 5 4 1 10
The table indicates, for example, that 80% of Good computers will have exactly 0 failures in 100 tests, while 70% of Defective computers have exactly 2 failures in 100 tests.
This is a hypothesis-testing situation.
Null hypothesis: computer is Good
Alternative hypothesis: computer is Defective.
The computer will be declared Defective (reject null hypothesis) if it fails at least 3 tests (3 or more).
Part a)
Suppose we test a computer and it fails 2 tests. What is the associated p-value?
Part b)
In this example what would a type I error be?
What is a consequence for the company if they make a type I error?
What is the probability of a Type I error?
Part c)
In this example what would a type II error be?
What is a consequence for the company if they make a type II error?
What is the probability of a Type II error?
Part d)
Do you think that the standard of declaring a computer Defective if it fails at least 3 tests (3 or more) is reasonable? Use the risk of type I and type II error to justify your opinion.
Answer by ikleyn(52795)   (Show Source):
You can put this solution on YOUR website! .
Wording in this problem is consistently incorrect, and if follow this wording literally,
then the problem is posed incorrectly.
To be correct, wording should be changed everywhere in the problem.
In other words, to be correct, the problem should be re-written from the scratch.
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