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Chapter 5 Sampling and Sampling Distributions

True/False Questions

1. A numerical measure of a sample is called a sample parameter.

Answer: False Type: Concept Difficulty: Easy

2. A single numerical value used to estimate one particular value of the population is apoint estimate.

Answer: True Type: Concept Difficulty: Easy

. The sample standard deviation! s! is a point estimate for .


". The standard error of the sample mean is e#ual to .


$. A sample si%e of & or more values is large enough for the Central 'imit Theorem to(e effective.


). As the sample si%e! n! increases! the sampling distri(ution of the sample proportion(ecomes less and less a normal distri(ution.


*. The sample mean is an un(iased estimate of the population mean.


+. A point estimate is a (iased estimator if its e,pected value is e#ual to the populationparameter it is estimating.


-. Estimator A is more efficient than estimator ! if Estimator A/s variance is smallerthan /s.

Answer: True Type: Concept Difficulty: 0edium

Aczel, Complete Business Statistics, Sixth Edition 1

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1&. The sample mean is a consistent estimator of .

Answer: True Type: Concept Difficulty: 0edium

11. A discrete random varia(le can tae on any value within its range and assignspro(a(ility %ero to any one given value.


12. The Central 'imit Theorem states that as the sample si%e increases! the distri(ution ofthe sample mean approaches a normal distri(ution with mean e#ual to the populationmean and standard deviation e#ual to the population standard deviation.

Answer: False Type: Concept Difficulty: 0edium

1. erforming a random sample means to hapha%ardly select the sample.


1". 3ampling error is the difference (etween the sample statistic and the populationparameter.


Multiple Choice Questions

1$. Following is a random sample of the heights of students in a class: $/4! $/-5! )/15!$/+5! $/115! )/$4! )/25! $/*5! $/15! )/! $/)5! $/-5. Compute a point estimate of the meanand the standard deviation of the heights of the students.A6 $/-.+4! 2.-46 $/1&.4! .""4C6 $/-.+4! 2.+4D6 $/1&.4! .14E6 none of the a(ove

Answer: E Type: Computation Difficulty: 0edium

2 Aczel, Complete Business Statistics, Sixth Edition

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1). A new shampoo is introduced in the maret. The manufacturer interviews 2$ differentindividuals for their opinion. Eighteen individuals lie the shampoo. Compute a point

estimate for the proportion of the population liing the shampoo.A6 &.)6 &.*2C6 &.2+D6 &.$)E6 &.)"

Answer: Type: Computation Difficulty: Easy

1*. 7n a certain town! a random sample of e,ecutives have the following personal incomes8in thousands69 $! "! 2-! $$! )! *2! 2+! ! )! "1! "2! $*! +! &. Compute point

estimates for the mean and the standard deviation of the incomes of the e,ecutives inthe town.A6 ""! 1.1&6 ""! 1.)"C6 "! 1.)D6 "$! 1&.**E6 "! 1.1

Answer: C Type: Computation Difficulty: 0edium

1+. 7n which of the following situations is the Central 'imit Theorem not applica(le

A6 ;hen the sample is small and the population is normal.6 ;hen the sample is large and the population is normal.C6 ;hen the sample is large! a(ove &! and the population is not normal.D6 ;hen the sample is small! (elow &! and the population is not normal.E6 none of the a(ove

Answer: D Type: Concept Difficulty: 0edium

1-. A certain (rand of electric (ul(s has an average life of && hours with a standarddeviation of 2$. A random sample of 1&& (ul(s is tested. ;hat is the pro(a(ility thatthe sample mean will (e less than 2-$

A6 &.&$"+6 &.1&-)C6 &.""$2D6 &.&*-E6 &.&22+



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2&. ;hen sampling from a population with a standard deviation of 1"! using a sample si%eof 1""! what is the pro(a(ility that the sample mean will (e at least units away from

the population meanA6 &.&&$16 &.&2$*C6 &.21$*D6 &.&1&2E6 &.&$1"

Answer: D Type: Computation Difficulty: 0edium

21. A particular camera is sold at an average price of

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2". The standard deviation of a random varia(le is:A6 always positive

6 always negativeC6 sometimes positive and sometimes negativeD6 depends on the mean of the random varia(leE6 none of the a(ove

Answer: A Type: Concept Difficulty: Easy

2$. The standard deviation of the average num(er of cassettes a college student owns is1". ;hat minimum sample si%e of students will give a sample standard deviation of atmost "A6 12

6 "C6 1D6 E6 1+


2). The average advertising e,penditure in the computer industry is found to (e is a normal random varia(le with mean 1& and standard deviation ".Then the pro(a(ility that > will (e greater than 12 is:A6 &.1$+*6 &."1

C6 &.&+$D6 &."**2E6 &.1-1$



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2+. The distri(ution of >! the num(er of cars sold per day! where > can (e &! 1! 2! ! "! or$! is:

A6 sometimes a normal distri(ution6 is normal if n! the num(er of days sampled! is at least &.C6 always a normal distri(utionD6 never a normal distri(utionE6 is a (inomial distri(ution


2-. A normal random varia(le is:A6 always symmetric6 never symmetric

C6 sometimes symmetricD6 symmetric if the mean is positiveE6 symmetric if the variance is large

Answer: A Type: Concept Difficulty: Easy

&. 3uppose that > is a normal random varia(le with mean 1* and standard deviation 1&.The pro(a(ility that the value of > will (e (etween ?2.) and ).) is:A6 &6 &.--C6 1

D6 &.-$E6 &.-&


1. ;hen sampling from a normal population with mean 1&& and standard deviation 12!using a sample si%e of )! the pro(a(ility that the sample mean will e,ceed 11& is:A6 &.2&6 &.*-)*C6 a very small num(erD6 a very large num(er

E6 a num(er very close to 1



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2. @n the average! 1+= of the population recycles their gar(age! with a standarddeviation of "=. @ut of a randomly selected ) households! how many will recycle

their gar(age on averageA6 1+6 )."+C6 -D6 $.&"E6 none of the a(ove

Answer: Type: Computation Difficulty: Easy

. The average telephone (ill in a locality is

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). 3uppose that > is a normal random varia(le with mean 2& and standard deviation .;hat is the pro(a(ility that a sample of ) taen has a mean of at least 1-

A6 a num(er very close to &.6 a(out &.$C6 a negative num(er.D6 a num(er very close to 1.E6 &.&22+


*. ;hen the pro(a(ility that an estimator is close to the parameter it estimates increasesas the sample si%e! n! increases! that estimator is said to (e:A6 un(iased

6 (iasedC6 efficientD6 consistentE6 sufficient


+. A poll of 1!$&& registered voters is taen. @f these! )&& say they will vote forcandidate 3mith. Compute a point estimate for the proportion of the population whowill vote for this candidate.A6 &.)&

6 &.&"C6 &."&D6 &.)E6 none of the a(ove

Answer: C Type: Computation Difficulty: Easy

-. ;hich of the following statements does not refer to the Central 'imit Theorem

A6 The e,pected value of the mean of the distri(ution of sample means is .

6 The distri(ution of sample means is appro,imately normally distri(uted.C6 The Central 'imit Theorem is true for any distri(ution! when the sample si%e is at

least &.D6 The standard deviation of the distri(ution of sample means is e#ual to .

E6 ;hen a non?normal population is sampled! the distri(ution of sample means isstill normally distri(uted! as long as the sample si%e is large.


Aczel, Complete Business Statistics, Sixth Edition

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"&. A certain (rand of tires has an average life of "$!&&& miles! with standard deviation of2!&&& miles. A random sample of ) tires is tested. ;hat is the pro(a(ility that this

sample will have a mean of at least ""!&&& milesA6 a num(er very close to %ero.6 a num(er very close to one.C6 a(out &.$D6 &.&+$E6 none of the a(ove

Answer: Type: Computation Difficulty: 0edium

"1. A population has a mean of -& and a standard deviation of 1$. A random sample of1&& is selected. ;hat is the standard error

A6 1$6 .+*C6 1.$D6 2.2$E6 none of the a(ove

Answer: C Type: Computation Difficulty: Easy

"2. The Bno?show5 rate at a popular resort hotel is +=. 7f a random sample of 1&&reservations is taen! what is the pro(a(ility that the num(er of Bno shows5 wille,ceed 1&

A6 &.&&"-6 &.1*++C6 &.22-)D6 &.**&"E6 &.+))$

Answer: Type: Computation Difficulty: ard

se the following to answer #uestions "?"$:

The relia(ility of a widely used microprocessor is typically e,pressed as time (etween failures

8TF6. 3uppose TF is an e,ponentially distri(uted random varia(le that averages !&&&cycles with a standard deviation of $".**) cycles.

1! Aczel, Complete Business Statistics, Sixth Edition

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". 7f a random sample of )" of these microprocessors is taen! what is the pro(a(ilitythat the sample average will (e (etween 2!--$ cycles and !&&$ cycles

A6 &.&*1+6 &.2&$2C6 &."1*)D6 &.")$"E6 &.$")


"". 3uppose a shipment of these microprocessors will (e reected if! after the drawing of arandom sample of si%e )! the sample average is less than 2!--+ cycles. ;hatproportion of shipments will (e reected

A6 &.12&6 &.2-$-C6 &."12-D6 &.""&"E6 &.")"1


"$. 3uppose the purchaser of these microprocessors will draw a random sample of si%e )!calculate a sample mean and standard deviation and then reect the shipment if thesample average falls (elow some agree?upon value. ;hat value would ensure that

appro,imately -$= of all shipments are acceptedA6 2!-+2.116 2!-+$.&*C6 2!-++.*$D6 !&1".-)E6 !&1*.++

Answer: Type: Computation Difficulty: ard


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"). The Tightward 0utual Funds Company (ills itself as BThe 'eader in 'ow?Fee Funds5(ased on a recent random sample of 1) of its funds that e,hi(ited a sample average of

"+ (asis points 81 (asis point is e#uivalent to a fee of &.&1=6. Assume that the fees ofTightwad/s competitors are normally distri(uted and average $& (asis points with astandard deviation of 12.$ (asis points. ;hat is the pro(a(ility that a random sampleof 1) funds from Tightwad/s competitors would have a lower sample average than "+A6 &.1&&6 &.2)11C6 &.*"$D6 &.")"E6 one of the a(ove

Answer: Type: Computation Difficulty: 0edium

se the following to answer #uestions "*?"+:

A manufacturer and one of its suppliers are engaged in negotiations regarding the inspectionplan for a component the supplier provides. Components will (e shipped in very large(atches! and random samples of $& will (e drawn for inspection. The manufacturer needscomponents to have an average length of )+ cm! with a standard deviation of " cm. othmanufacturer and supplier have agreed that there should (e no more than a $= chance ofreecting a shipment that conforms to this specification.

"*. A policy in which a sample mean of leads to a reected shipment will

ensure only there is appro,imately a $= ris of a conforming shipment/s (eingreected.A6 'ess than )*.&* cm6 'ess than )1."$ cmC6 Greater than )+.- cmD6 Greater than *".*& cmE6 one of the a(ove

Answer: A Type: Computation Difficulty: ard


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"+. 3uppose that a particular shipment actually has an average length of )- cm! with astandard deviation of 1) cm. 7f the decision rule is to reect the shipment if its sample

average is in e,cess of *1 cm! how liely is it that this shipment will (e reectedA6 &.)*&&6 &.""+C6 &.22))D6 &.1+-"E6 one of the a(ove


"-. 7f the Central 'imit Theorem is applica(le! this means that the sampling distri(ution ofa population can (e treated as normal since the is

.A6 on?normal9 sample si%e9 small6 on?symmetrical9 variance9 largeC6 laty?urtotic9 sample si%e9 largeD6 inomial9 variance9 largeE6 on?normal9 standard error9 large

Answer: C Type: Concept Difficulty: 0edium

$&. Transportation authorities consider a particular 1)?passenger airplane to (e overloadedif the total carried e,ceeds 2!)"& pounds. 3uppose that the load placed on a plane (y a

typical passenger is normally distri(uted with a mean of 1$$ pounds and a standarddeviation of & pounds. 7f passengers are typically assigned randomly to flights!without regard for their particular load! what proportion of flights will (e overloadedA6 &.&-1+6 &.*&*C6 &.)2-D6 &.-&+2E6 Cannot (e determined from information given

Answer: A Type: Computation Difficulty: ard


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Short Answer Questions

$1. Following is a random sample of the heights of students in a class: $/4! $4-4! )/15!$/+5! $/115! )/$5! )/25! $/*5! $/115! )/! $/)4! $/-4. Estimate the proportion of studentswith heights more than ) feet.

Answer: 1H" ? count num(er of heights over )/ I H12 I 1H" Type: ComputationDifficulty: Easy

$2. 7n a certain town! a random sample of e,ecutives has the following personal incomes8in thousands69 $! "! 2-! $$! )! *2! 2+! ! )! "1! "2! $*! +! &. Find an estimatefor the proportion of e,ecutives with income greater than

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$*. A random sample of si%e 2* is collected and the mean is computed. ;hat is the totalnum(er of degrees of freedom for deviations from the mean

Answer: 2) ? n ?1 I 2*! 1 I 2) Type: Concept Difficulty: Easy

$+. The average profit stores mae on the sale of a particular computer is

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)2. Find the mean! variance! and standard deviation of these data.

Answer: 0ean: -.-*2$9 Lariance: .&&$-9 3tandard Deviation: .&*" Type: ConceptDifficulty: Easy

). The (ottling machine is designed to dispense an average of 1& ounces per (ottle! witha standard deviation of .$ ounce. 7f the machine is operating properly! what is thepro(a(ility of finding a sample of 1) (ottles with a mean as small or smaller than themean of this sample

Answer: ."12- Type: Concept Difficulty: 0edium

)". 0ature poppy plants are e,pected to have an average height of 1) inches! with a

standard deviation of inches. ;hat/s the pro(a(ility that a sample of )" poppies willhave an average height of (etween 1$ and 1* inches

Answer: &.--2" Type: Concept Difficulty: 0edium

)$. lasma display units undergoing a coating operation have an average re#uired curingtime of +.$ seconds. E,perience has (een shown the re#uired curing time to (enormally distri(uted with a standard deviation of 12 seconds. 7f 1& units are drawn atrandom! what is the pro(a(ility that the sample average for re#uired drying time will(e no less than +& seconds (ut no more than +$ seconds

Answer: &."*)) Type: Computation Difficulty: 0edium

)). 'aggardAir! which is (urdened with one of the worst on?time records in the airlineindustry! still sees many of its flights depart on time. 3uppose representatives from anair travelers/ advocacy association are coming to e,amine 'aggardAir/s records. Arandom sample of $& flight records will (e drawn! and if +&= or more show an on?time departure! 'aggardAir will (e given the association/s unctuality Award. ;hat isthe pro(a(ility that 'aggardAir will (e given the unctuality Award even if its actualon?time rate is only )&=

Answer: &.&&1- Type: Computation Difficulty: 0edium

)*. Mohnny Appleseed Grocery monitors its C data?lining process closely. Each itemscanned at checout is priced either correctly or incorrectly! depending on how wellthe C data?lining process is performing. 3uppose a recent sample of 1!$&& itemscans indicated 1) that lined incorrectly. Assuming the data?lining process is --.=accurate! what was the pro(a(ility of o(serving a mislin rate that high or higher

Answer: &.&"") Type: Computation Difficulty: 0edium


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