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Dear allstat,
I need your help so as to double check the answer for the following case
study:-
There are only a few laboratories across the country that test consumer
products. UNDERWRITERS LABORATORIES OF CHENGAL is the best known. GAJAH SEWA
LABORATORIES is another of these testing organizations and it is located in
DAYAK, OMPENG.
POAD SABER is the chief testing engineer for the company and supervises the
work of seven other engineers. The engineers have between four and six
testing technicians reporting to each of them. If a company wishes to obtain
the GAJAH SEWA of approval from the laboratory to display on its products,
it must allow a laboratory technician to come to its plant, randomly select
items from the production line and bring them back to DAYAK for testing. The
tests involve examining the items to see that they meet their design
specifications and federal or local safety standards.
For instance, a clock radio might be tested to make sure that the clock
keeps reasonably accurate time, the alarm goes off when it is set, the case
is shockproof, and the circuitry has been connected just as the electrical
schematic diagram shows it should be. Many items are tested for parts
reliability. That is, an electrical appliance might be operated continuously
for several hundred hours or until it breaks down in order to determine the
operating life of the item.
Mr Saber has just received some data on UTARA LAMPU LTD's new ornamental
outdoor arc lamp. The lamp is used on a post in the front yards of
homeowners living on poorly lighted streets. UTARA's lamp sells for a
substantially higher price than the conventional lamps used for this
purpose. However, it lights a much wider area and UTARA believes that it
lasts much longer. Unfortunately, UTARA has no hard data to prove this
second claim. Sales of the lamp have been slow since the competition has
been successful in making dealers believe that UTARA's lamp is too expensive
and has a rather short life. Nearly two years ago GAJAH SEWA was asked to
bid on the cost of testing some of UTARA's arc lamps. Since UTARA wanted to
advertise the length of life of their lamp to dealers, they felt it
necessary to use an independent testing agent.
GAJAH SEWA won the contract to perform the tests. A GAJAH SEWA technician
visited SG LEMBING plant of UTARA LAMPU and randomly selected 20 lamps for
testing. The lamps were wired to a special control board that regulated the
amount of time the lamps were lighted. This automatic board turned on all
the lamps simultaneously and left them on for a randomly determined period
of time but the time was controlled so that it never exceeded 12 hours of
continuous operation. When the lights were turned off, the control board
monitored their temperature. Once the light cooled to room temperature, they
were turned on again for another randomly determined period.
When a lamp burned out, a small alarm sounded and a technician recorded from
timer mounted on the control board, the total amount of time the lamp had
been operated. The test data showing the times until failure for all 20
lamps are shown in the accompanying table. All that remains is for Mr. SABER
to write his report to UTARA LAMPU concerning the length of life that can be
expected from all their arc lamps. In his report Mr. SABER intends to note
that 8 of 40 lamps in a separate study had popped, cracked or exploded when
they failed. Since such events might involve a hazard to lamp users, he
intends to make an estimate of the extent to which this characteristic can
be expected among UTARA's new arc lamps.
Item No. Hours to Failure Item No. Hours Failure
1 13,140 11 14,990
2 17,555 12 7,901
3 9,490 13 13,893
4 8,090 14 15,737
5 12,234 15 12,459
6 13,876 16 13,952
7 14,570 17 9,333
8 18,442 18 10,873
9 11,109 19 11,537
10 14,007 20 10,755
Questions:
(a) Find a 95% confidence interval for the mean time to failure.
(b) Find a 95% confidence interval for the proportion of lamps that exhibit
cracking, popping or exploding on failure.
Please reply to [log in to unmask]
Thank you
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