7/27/2019 Exercises on Tests of Hypothesis.pdf
1/4
Exercise Set for l ec tu re ' "1. A major car manufacturer wants
to test a new engine to determine whether it meets new air
pollution
standards. The mean emission of all engines of this type must be
less than 20 parts per million of carbon.Ten engines are
manufactured for testing purpose, and the emission level of each is
determined. The dataare listed below:15.6 16.2 22.5 20.5 16.4 19.4
16.6 17.9 12.7 13.9Do the data supply evidence to allow the
manufacturer to conclude that this type of engine meets thepollut
ion standard? Assume that the production process is stable and the
manufacturer is willing to risk aType I error with probability
0.01.
2. The reputations (and hence sales) of many businesses can be
severely damaged by shipments ofmanufactured items that contain a
large percentage of defectives. For example, a manufacturer
ofalkaline batteries may want to be reasonably certain that fewer
than 5% of its batteries are defective.Suppose 300 batteries are
randomly selected from a very large shipment; each is tested and 10
defectivebatteries are found. Does this provide sufficient evidence
for the manufacturer to conclude that thefraction defective in the
entire shipment is less than 0.05? Use a 0.01 significance
level.
3. A local pizza parlor advertises that their average time for
delivery of pizza is within 30 minutes of receiptof the order. The
delivery times for random sample of 60 orders were recorded, with
the followingresults: x-bar:; 34 minutes; s :; 21 minutes. Is there
sufficient evidence to conclude that the actual meandelivery time
is larger than what is claimed by the pizza parlor? Use a
significance level of 0.01.
4. A machine is designed to fill cereal boxes with a net weight
of 16 ounces. It is important that the machineoperate accurately:
if it fills too much, the company wastes excess cereal; if it
underfills the boxes, thecompany risks a penalty from the Food and
Drug Administration. The company has instituted a newquality
control program to monitor the amount of fill of its cereal boxes.
Every four hours, a randomsample of 100 boxes is select'ed from the
production line, and the amounts of fill are noted. If there
isevidence (at 5% significance) that the mean amount of fill
differs from 16 ounces, then the filling machineis reset. Suppose
one such inspection yielded the following results: x-bar:; 15.98
ounces; s :; .21 ounce.Should the machine be reset?
5. A transcoceanic airline conducted a study to determine
whether the mean weight of the baggage checkedby a passenger on its
Miami to London flight differs significantly f rom 45 pounds. A
random sample of 25passengers was selected, and the weight of each
passenger's checked baggage was recorded. Thefollowing results were
obtained: x - bar =43.5 pounds; s 6 pounds. If the airline is
willing to risk a Type 1error with probability 0.05, what should
they conclude from th is study?
6. Refer to question 3 and const ruct a 95% confidence interval
fo r the true mean weight of checked baggageof passengers on the
Miami to London flight.
7. In previous years, a mail order company observed that 10% of
its customers placed an additional orderwithin six months of their
original order. However, the records fo r a random sample of 1000
recentcustomers indicated that only 80 customers placed an
additional order within six months of their originalorder. Is there
evidence (at 5% significance) that the propor tion of customers who
place additional ordershas decreased from previous years?
8. A national retail chain wishes to estimate p, the proportion
of charge customers who are more than onemonth behind in their
payments. If they want to be 95% confident that their estimate is
within 0.01 of thetrue value of p, how many accounts should be
sampled? (Past evidence indicates that the proportion ofdelinquent
accounts is approximately 0.15.)
7/27/2019 Exercises on Tests of Hypothesis.pdf
2/4
1(I)".---"- - - . - . ~ / 1x..= rf1 ' l ,He : p.:: 0 1A-:::
2QgH(:.. : p. C. ~ D 1
11~ / ~
R Ho { t t.. - 2 ' 2. !{ I 1-::::> ~ L.{.e H > ~
t-,---z.c:.-2.'n
" , , ~ . .' f> ; f, .It '. '
..,L .:,- v - a i l r
, ~ t l " ~ ~ { " (4 j \ tLQ!-A!"J ck , " " , hv" .. ~ """,*
Q"",MMU' ;.k trD! }t"CA.AA : ;: I "-\ 0' . t t ' ~ Ah ,:,."J;.. , ~
. h . ~ . . k ~ ~ t < < v " ' + ~;:UA {f - 1 , . , ~ "b ~
vu.V> .
"
7/27/2019 Exercises on Tests of Hypothesis.pdf
3/4
lto) ~ - . : : . >01-\,. : t-.J.) SOl -
.:::)
~ a }" .' ~ " ---- : : ~ t ' . ' 1 5 ;;> - t, i 6........._,
. 0) . 1 Ivro')
, J h ' ~ r1'ceA..AA c ~ .:.! ,) ..... \- ~ e.. c{.... , ~ . . ~
- - 1 ' C eA..
t .. " ..LJ }-D ~ . e . t ! t ! JN " , . iLl ' j '.J.. .. cU:
!7h,cU t , : l h " ~ ~ d.2
!J'\' \
\-! ., '0
t... -0{.06!'f. r 2 Db ' f tl"'f i-I
