Fried PCs. A computer company recently experienced a disastrous fire that ruined some of its inventory. Unfortu-nately, during the panic of the fire, some of the damaged computers were sent to another warehouse, where theywere mixed with undamaged computers. The engineerresponsible for quality control would like to check outeach computer in order to decide whether it’s undamagedor damaged. Each computer undergoes a series of 100tests. The number of tests it fails will be used to makethe decision. If it fails more than a certain number, it willbe classified as damaged and then scrapped. From pasthistory, the distribution of the number of tests failed isknown for both undamaged and damaged computers.The relative frequencies of each outcome are listed in thetable below:The table indicates, for example, that 80% of theundamaged computers have no failures, while 70% ofthe damaged computers have 2 failures.a) To the engineers, this is a hypothesis-testing situation.State the null and alternative hypotheses.b) Someone suggests classifying a computer as damagedif it fails any of the tests. Discuss the advantages anddisadvantages of this test plan.c) What number of tests would a computer have to fail inorder to be classified as damaged if the engineers wantto have the probability of a Type I error equal to 5%?d) What’s the power of the test plan in part c?e) A colleague points out that by increasing a just 2%,the power can be increased substantially. Explain. Number of tests failed 0 1 2 3 4 5 +5Undamaged (%) 80 13 2 4 1 0 0Damaged (%) 0 10 70 5 4 1 10

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Fried PCs. A computer company recently experienced a

disastrous fire that ruined some of its inventory. Unfortu-
nately, during the panic of the fire, some of the damaged

computers were sent to another warehouse, where they
were mixed with undamaged computers. The engineer
responsible for quality control would like to check out
each computer in order to decide whether it’s undamaged
or damaged. Each computer undergoes a series of 100
tests. The number of tests it fails will be used to make
the decision. If it fails more than a certain number, it will
be classified as damaged and then scrapped. From past
history, the distribution of the number of tests failed is
known for both undamaged and damaged computers.
The relative frequencies of each outcome are listed in the
table below:The table indicates, for example, that 80% of the
undamaged computers have no failures, while 70% of
the damaged computers have 2 failures.
a) To the engineers, this is a hypothesis-testing situation.
State the null and alternative hypotheses.
b) Someone suggests classifying a computer as damaged
if it fails any of the tests. Discuss the advantages and
disadvantages of this test plan.
c) What number of tests would a computer have to fail in
order to be classified as damaged if the engineers want
to have the probability of a Type I error equal to 5%?
d) What’s the power of the test plan in part c?
e) A colleague points out that by increasing a just 2%,
the power can be increased substantially. Explain.

Number of tests failed 0 1 2 3 4 5 +5
Undamaged (%) 80 13 2 4 1 0 0
Damaged (%) 0 10 70 5 4 1 10

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