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BES Tutorial Sample Solutions, S1/10
WEEK 13 TUTORIAL EXERCISES (To be discussed in the week starting
May 31)
1.
It is claimed by a manufacturer that its new type of light bulb is subject
to less variability of bulb life. It is known that the former bulb type had
a standard deviation of life of 150 hours. To test this claim, a consumer
organization takes a sample of 41 of these new bulbs and measures
their lives, finding a standard deviation of bulb life of 140 hours.
Assuming light bulb lives are approximately normally distributed, test
the manufacturer’s claim at a 5% level of significance.
n = 41, s = 140
ܪ
:ߪ
ଶ
ൌ 150
ଶ
; ܪ
ଵ
ଶ
൏ 150
ଶ
Under
ܪ
ሺ݊െ1ሻݏ
ଶ
ߪ
ଶ
ൌ
40 ൈ ݏ
ଶ
150
ଶ
~߯
ସଵିଵ
ଶ
Decision rule:
Reject
ܪ
if
݈ܿܽܿݑ݈ܽݐ݁݀ ߯
ଶ
൏߯
.ଽହ,ସ
ଶ
ൌ 26.5093
Since calculated
߯
ଶ
ൌ
40 ൈ 140
ଶ
150
ଶ
ൌ 34.84 ߯
.ଽହ,ସ
ଶ
ൌ 26.5093
we do not reject
ܪ
and conclude that the manufacturer’s claim of lower bulb
life variability is not supported by the data.
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 Three '11
 DenzilGFiebig

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