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Class Time_______________
Day_____________________
School of Business
Business Statistics I
Exam 5
Print out this test. Do all your calculations on
the test and mark your final
answer on the scantron sheet(answer sheet. If
you don’t have a scantron sheet,
one will be provided in the class.Turn‐in both your
test and the answer sheet. Do
not forget to writeyour name, Id#, and class time on
both the answer sheetand
the test.
Name____________________________________ID #________
______
1.
Suppose a random sample of 36 items is selected from a populat
ion. The population
standard deviation is known to be 10. The standard error of the
mean would be:

(a) 1.333
(b) 1.667
(c) 3.667
(d) 2.333
(e) 1.875
2.
From 100 homes of similar sizes, a sample of 25 homes is select
ed to study the average
home heating cost during the winter months. Suppose the heatin
g cost is known to be
normally distributed with mean of $220 per month for the four
months of winter and
standard deviation of $45. If the 100 homes represent the popula
tion size, the standard
error of the heating cost would be:
(a) 9.00
(b) 8.75
(c) 3.66
(d) 7.83
(e) 1.87
3. Suppose n=64 measurements is selected from a
population with mean and
standard
. The Z‐score corresponding to a value of would be:
(a) 2.0
(b) 3.0
(c) ‐2.5
(d) ‐2.0
Page 2 of 10

(e) 1.5
4.
A random sample of n=100 observations is selected from a popu
lation with and
standard The probability that is
(a) 0.8236
(b) 0.8936
(c) 0.9036
(d) 0.9983
(e) 0.8944
5.
A random sample of n=100 observations is selected from a popu
lation with and
standard The probability that (22.1 26.8)p
is
(a) 0.0434
(b) 0.0228
(c) 0.0036
(d) 0.0983
(e) 0.0944
6.
A random sample of size 36 is drawn from a population with me
If 86% of
the time the sample mean is less than 281, then the
population standard deviation
would be:
(a) 16.67
(b) 12.67
(c) 11.12

(d) 13.33
(e) 19.67
7.
A random sample of size n=81 is drawn from population with m
ean equal to 50 and
standard deviation 25. The expected value of the mean ( )iE x
and the standard
error
x
(a) 50 and 2.95
(b) 50 and 2.78
(c) 28 and 1.72
(d) 50 and 15.00
(e) 80 and 12.0
8.
According to a recent news report, the average price of gasoline
is $3.80 per gallon
(March 2011). This price can be considered as the nationwide p
opulation mean price
per gallon. Suppose that the standard deviation of the
gasoline price per gallon is
$0.50. A sample of 49 gas stations in Salt Lake City is taken. T
he probability that the
sample mean price is within ±0.10 of the population mean is
(a) 0.9236
(b) 0.8384
(c) 0.9544
(d) 0.9983

of 10
(e) 0.8764
9. A finite population is normally distributed with mean
and standard deviation
. Suppose a sample of size 49 is taken so that the sample mean
x can be used to
estimate the population mean
The probability that the sample mean is less than or
equal to 48 or,
if the size of the finite population is N=150
(a) 0.1236
(b) 0.2420
(c) 0.1544
(d) 0.1983
(e) 0.1292
10.
The average life of a battery used in newly designed electric car
s is 150 hours with a
standard deviation of 20 hours. Suppose these values are true fo
r all batteries of this
type so that these values can be considered true for the populati
on with μ = 150 and σ
= 20. If a sample of size 50 is selected, the probability that the
sample mean life is
within ± 5 of the population mean (between 145 and 155 hours)
is
(a) 0.8236
(b) 0.9420
(c) 0.9544
(d) 0.9232
(e) 0.1292

11.
The production manager of a bottling plant has acquired new ma
chines to fill beverage
cans. These machines are used to fill 16 ounce cans in one of th
eir production lines. If
the filling machine
is working properly, the mean fill volume should be 16.0
ounces
with a standard deviation of 0.30 ounces. If mean fill volume in
the cans is over 16.2
ounces or below 15.8 ounces, then an over filling or under fillin
g occurs. To avoid over
or under filling the production manager randomly selects
a sample of 9 cans
periodically and checks the volume. If the average content is les
s than 15.8 ounces or
more than 16.2 ounces, the production manager must stop
the line to make
adjustments. The probability of stopping the line based on the i
nformation above is:
(a) 0.0236
(b) 0.0376
(c) 0.0400
(d) 0.0456
(e) None of the above
12.
A new Rasmussen Report national telephone survey finds that
just 32% of American
Adults favor “sin taxes” on soda and junk foods. The survey wa
s based on a sample of
1,000 American Adults. Based on this survey data, the standard

deviation of p or the
standard error of sample proportion would be (considering
(a) 0.0176
(b) 0.0200
(c) 0.0196
(d) 0.0148
Page 4 of 10
(e) 0.0138
13. Based on a report, 55% of the voters believe that the
nation’s current economic
problems are the result of recession that started during the Bush
administration. A
new Rasmussen Reports national telephone survey finds that 51
% of likely voters say
the nation’s current economic problems are due to the recession
which began under
the administration of George Bush. This survey was based on 1,
000 likely voters and
was conducted on March 18‐19, 2011 by Rasmussen
Reports. Based on this survey
report, the probability that the sample proportion is lower than
51% is approximately
(a) 0.0076
(b) 0.0200
(c) 0.0055
(d) 0.0098
(e) 0.0128

14.
According to a newly published report approximately 43% of ad
ults say filing their
tax paperwork is worse than a trip to the dentist. If a random sa
mple of 200 is
chosen, the probability that at least 90 of them share this opinio
n is
(a) 0.2076
(b) 0.3200
(c) 0.0155
(d) 0.2843
(e) 0.3128
15. A study about the students graduating within 4 years
of their entrance to the
universities indicated that 62% of the students do not
graduate within 4 years.
Suppose a random sample of 500 students was taken. The sampl
e considered the
students after 4 years of their college entrance. The probability
that fewer than 285
graduated within 4 years is
(a) 0.4893
(b) 0.9893
(c) 0.0107
(d) 0.0584
(e) 0.0628
16. Historically, a production line produces 6% defective
items. The production
supervisor takes a sample of 100 items frequently and if he find
s 8 or more defective
products, he stops the line to make adjustments. The
probability that a random

sample of 100 would lead to the stoppage of the production line
is:
(a) 0.2995
(b) 0.3893
(c) 0.2005
(d) 0.4584
(e) 0.7995
17. In simple random sampling
(a) Every sample has equal probability being selected
(b) Every sample is drawn at a pre‐specified time
Page 5 of 10
(c) Every item in the sample has equal probability
(d) None of the above is correct
(e) Only (a) and (c) are correct
18.
From a population of size 8 (N=8), all possible samples of size
3 (n=3) that can be drawn
are:
(a) 24
(b) 15
(c) 10
(d) 56
(e) 86
19.
A confidence interval for the mean is determined using the follo
wing formula

1.28x
n
The confidence level being used in the above interval is
(a) 95%
(b) 98%
(c) 99%
(d) 67%
(e) 80%
20.
A confidence interval for the mean is determined using the follo
wing formula
0.99x
n
The confidence level being used in the above interval is
(a) 95.52%
(b) 98.32%
(c) 33.89%
(d) 67.78%
(e) 80.56%
21.

In a confidence interval, increasing the confidence level while k
eeping the sample size
fixed
(a) increases the width of the confidence interval.
(b) leaves the confidence interval unchanged.
(c) makes the confidence interval estimate more precise.
(d) makes the confidence interval estimate more reliable.
(e) decreases the width of the confidence interval.
22. The general form of a confidence interval is
(a) Point estimate ± standard error.
(b) Mean ± standard error of the mean.
(c) Mean ± the margin of error.
(d) Point estimate ± the margin of error.
Page 6 of 10
(e) Estimate ± the margin of error.
23. A random sample of n measurements is selected from
a population with unknown
mean and known standard deviation
. A 95% confidence interval for when
200, 102, 4.69n x be
(a) 104.35 and 15.65.
(b) 103.76 and 134.24
(c) 101.35 and 102.65
(d) 108.56 and 120.44
(e) 118.25 and 123.75
24. A random sample of size 20 produced a sample mean
and a standard

deviation
A 80% confidence interval using a t‐distribution is to be constr
ucted.
The t‐ value for the interval would be
(a) 1.711
(b) 2.064
(c) 2.038
(d) 1.328
(e) 2.485
25.
In constructing a confidence interval with known population sta
ndard deviation the
sample size is increased from n=36 to n=144 while the confiden
ce level is held fixed at
95%. This will
(a)
increase the width of the confidence interval making the estimat
e less precise.
(b)
decrease the width of the confidence interval making the estimat
e less precise.
(c) leave the width of the confidence interval unchanged.
(d) double the width of the confidence interval.
(e)
decrease the width of the confidence interval making the estimat
e more precise.
26. In constructing a confidence interval with known
population standard deviation
the sample size is increased from n=64 to n=256 while the conf
idence level is
held fixed at 95%. This will
(a) decrease the width of the confidence interval by 75%.
(b) leave the width of the confidence interval unchanged.

(c) double the width of the confidence interval.
(d) reduce the width of the interval to one‐half.
(e) Increase the width of the interval by 100%.
27.
The length of time that a space rocket component functions is a
pproximately normally
distributed. A sample of 20 of these components showed a mean
of hours
with a standard deviation
hours. A 95% confidence interval for the mean time
that the component will function is to be constructed. The margi
n of error would be
(a) 42.9
(b) 40.7
(c) 81.4
(d) 34.2
(e) Can’t be determined
Page 7 of 10
28.
The length of time that a space rocket component functions is a
pproximately normally
distributed. A sample of 20 of these components showed a mean
of hours
with a standard deviation
hours. A 95% confidence interval for the mean time
that the component will function
(a) 824.94 to 927.06
(b) 724.94 to 927.46
(c) 823.45 to 928.55

(d) 859.3 to 940.7
(e) 824.00 to 927.06
29.
The standard deviation of the test scores on a certain college pla
cement test is known
to be 12.5. A random sample of 81 students had a mean
score of 86.8. A 90%
confidence interval estimate for the average score of all student
s is
(a) 82.94 to 92.06
(b) 84.52 to 89.08
(c) 82.45 to 92.55
(d) 85.32 to 94.68
(e) 84.00 to 92.70
30. Which of the following statement is true for
constructing the confidence interval
estimate for the population mean
(a)
higher is the confidence interval, wider is the confidence interv
al for a fixed sample
size.
(b)
larger is the sample standard deviation, wider is the confidence
interval when the
sample size and confidence level are fixed
(c) in cases where the population standard deviation is
known, the appropriate

distribution to use to construct the interval is the normal distrib
ution.
(d) In a confidence interval, the margin of error gets
larger as the sample size is
increased.
(e) all of the above statements are true.
31.
The average life of a sample of 30 car tires was found to be 60,0
00 miles. It is known
that the
lifetimes of such tires are normally distributed with a standard d
eviation of
7,500 miles. A 95% confidence interval estimate of the mean lif
e of all such tires was
calculated. The width of this confidence interval is
(a) 5937
(b) 5368
(c) 6357
(d) 5731
(e) 5846
32.
The Nielsen Company reported that as of the third quarter of 20
10, 28 percent of U.S.
mobile subscribers now have smart phones, cell phones
with operating systems
Page 8 of 10

resembling those of computers. The growing popularity of smart
phones like Apple’s
iPhone, RIM’s Blackberry devices and a variety of Google Andr
oid‐based models on the
market, has accelerated the adoption rate. Among those
who acquired a new cell
phone in the past six months, 41 percent opted for a
Smartphone over a standard
feature phone. A sample of 850 high school students was asked
if they had a smart
phone. An overwhelming 578 indicated that they had a smart ph
one. The margin of
error at a 95% confidence would be
(a) 0.02
(b) 0.05
(c) 0.03
(d) 0.09
(e) 0.06
33.
Approximately 51 percent of the U.S. population has at least tw
o credit cards. (Source:
Experian national score index study, February 2007). Suppose a
study of 500 consumers
showed that 315 carried three or more credit cards. A 95% conf
idence interval for the
proportion of U.S. population who carried three or more credit c
ards would be
(a) 0.588 to 0.734
(b) 0.598 to 0.689
(c) 0.633 to 0.732
(d) 0.588 to 0.672
(e) 0.355 to 0.896

34.
The following expressions are for the confidence intervals for th
e mean:
20
100 (2.0)
100
20
100 (2.0)
400
Note that the difference between the two intervals is that the sa
mple size in the second
interval is four times large compared to the first interval. What i
s the effect on the width
of the confidence interval of quadrupling the sample size
while holding all the other
data fixed?

(a) increase the width of the confidence interval by 75%.
(b) increase the width of the confidence interval by one‐half.
(c) decease the width of the confidence interval to one‐third.
(d) leave the width of the confidence interval unchanged.
(e) reduce the width of the confidence interval by one one‐half.
Page 9 of 10
35.
A quality engineer is interested in estimating the mean time req
uired to assemble a bar
code scanner. If the engineer wishes to be 95% confident that th
e error in estimating
the mean time is less than 0.25 minutes, and she knows from the
past experience that
the standard deviation of the assembly time is 0.75 minutes; the
sample size she would
need is
(a) 20
(b) 24
(c) 25
(d) 35
(e) 30
36.
The required sample size to estimate the mean for an a particula
r study resulted into
significantly large sample size. The analyst believes that he doe
s not have the time or
the resources to collect such a large sample. Which of the follo

wing actions would lead
to a reduced sample size?
(a)
the margin of error required in the actual study should be increa
sed.
(b) the confidence level should be reduces.
(c) the variation in the population should be reduced.
(d) all of the above will lead to a reduced sample size.
37. A large hospital wants to estimate the mean time
before the patients are attended
upon arrival to the hospital emergency room. From a past study,
it is known that the
standard deviation of the waiting time is 12 minutes. If
the hospital administration
wishes to estimate the mean time within 3 minutes with a 95% c
onfidence, the sample
size needed will be
(a) 107
(b) 190
(c) 500
(d) 62
(e) 290
38.
A manufacturer of plasma TVs has problems with excessive cust
omer complaints and
consequent return of the product for repair or
replacement. The quality control
department wants to determine the magnitude of the problem so
that it can estimate
its warranty liability. The number of
plasma TVs the quality engineer should sample
and inspect in order to estimate the fraction defective, p
within 2% with a 95%

confidence would be
(a) 2500
(b) 2401
(c) 3000
(d) 2000
(e) 5300
Page 10 of 10
39. A manufacturer of electronic chip is interested in
estimating the fraction defective
chips produced in one of their plants. A random sample
of 200 chips produced 12
defectives. The point estimate and a 95% confidence interval on
the fraction defective
would be
and 95% confidence interval
(d) 0.06p and 95% confidence interval
(e) None of the above.
40.
The poll conducted by media and other agencies use a 95% conf
idence unless specified
otherwise. A 95% confidence interval for p
at a 95% confidence is given by

(1 )
1.96
p p
p
n
Where n is the sample size.
is the proportion of those in the sample
who approve of the way the President is handling the economy.
If the margin of error is
±3 percent, the sample size used in the study was
(a) 735
(b) 840
(c) 984
(d) 649
(e) 526
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/HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za
visokokvalitetni ispis prije tiskanja koristite ove postavke.
Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe
Reader 5.0 i kasnijim verzijama.)

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/NLD (Gebruik deze instellingen om Adobe PDF-documenten
te maken die zijn geoptimaliseerd voor prepress-afdrukken van
hoge kwaliteit. De gemaakte PDF-documenten kunnen worden
geopend met Acrobat en Adobe Reader 5.0 en hoger.)
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6c00610020006a0061002000410064006f0062006500200052006
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006a006100200075007500640065006d006d0069006c006c00610
02e>
/SVE
<FEFF0041006e007600e4006e00640020006400650020006800e
4007200200069006e0073007400e4006c006c006e0069006e0067
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06500730073002d007500740073006b0072006900660074002000
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400650074002e002000200053006b006100700061006400650020
005000440046002d0064006f006b0075006d0065006e007400200
06b0061006e002000f600700070006e0061007300200069002000
4100630072006f0062006100740020006f0063006800200041006
4006f00620065002000520065006100640065007200200035002e

00300020006f00630068002000730065006e006100720065002e>
/TUR
<FEFF005900fc006b00730065006b0020006b0061006c0069007
40065006c0069002000f6006e002000790061007a006401310072
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00620065006c00670065006c00650072006900200041006300720
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2000520065006100640065007200200035002e003000200076006
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0020007300fc007200fc006d006c00650072006c00650020006100
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/UKR
<FEFF04120438043a043e0440043804410442043e04320443043
9044204350020044604560020043f043004400430043c04350442
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/ENU (Use these settings to create Adobe PDF documents
best suited for high-quality prepress printing. Created PDF
documents can be opened with Acrobat and Adobe Reader 5.0
and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK

/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice

Page 1 of 10 ClassTime_______________Day_____________.docx

Page 1 of 10 ClassTime___Day_.docx

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