TestBank ForProbabilityAnd Statistics ForEngineering
s ss s s ss ss s
And The Sciences 8th Ed by Jay L. Devore.
ss ss ss ss ss ss ss ss ss
,
,Chapter 1 – Overview and Descriptive Statistics
ss ss ss ss ss ss
SHORT s s ANSWER
1. Give s s one s s possible s s sample s s of s s size s s 4 s s from s s each s s of s s the s s following s s populations:
a. All s s daily s s newspapers s s published s s in s s the s s United s s States
b. All s s companies s s listed s s on s s the s s New s s York s s Stock s s Exchange
c. All s s students s s at s s your s s college s s or s s university
d. All s s grade s s point s s averages s s of s s students s s at s s your s s college s s or s s university
ANS:
a. Houston s s Chronicle, s s Des s s Moines s s Register, s s Chicago s s Tribune, s s Washington s s Post
b. Capital s s One, s s Campbell s s Soup, s s Merrill s s Lynch, s s Pulitzer
c. John s s Anderson, s s Emily s s Black, s s Bill Carter, s s Kay s s Davis
d. 2.58. s s 2.96, s s 3.51, s s 3.69
PTS: 1
2. A s s Southern s s State s s University s s system s s consists s s of s s 23 s s campuses. s s An s s administrator s s wishes
ss to s s make s s an s s inference s s about s s the s s average s s distance s s between s s the s s hometowns s s of s s students
s s and s s their s s campuses. s s Describe s s and ssdiscuss s s several s s different s s sampling s s methods s s that s s might
s s be s s employed. s s Would s s this s s be s s an s s enumerative s s or s s an ssanalytic s s study? s s Explain s s your
s s reasoning.
ANS:
One s s could s s take s s a s s simple s s random s s sample s s of s s students s s from s s all s s students s s in s s the s s California
s s State s s University sssystem s s and s s ask s s each s s student s s in s s the s s sample s s to s s report s s the s s distance
s s from s s their s s hometown s s to s s campus.
Alternatively, s s the s s sample s s could s s be s s generated s s by s s taking s s a s s stratified s s random s s sample s s by
s s taking s s a s s simple ssrandom s s sample s s from s s each s s of s s the s s 23 s s campuses s s and s s again s s asking s s each
s s student s s in s s the s s sample s s to s s report s s the ssdistance s s from s s their s s hometown s s to s s campus.
Certain s s problems s s might s s arise s s with s s self s s reporting s s of s s distances, s s such s s as s s recording s s error s s or
s s poor s s recall. s s This ssstudy s s is s s enumerative s s because s s there s s exists s s a s s finite, s s identifiable
s s population s s of s s objects s s from s s which s s to s s sample.
PTS: 1
3. A s s Michigan s s city s s divides s s naturally s s into s s ten s s district s s neighborhoods. s s How s s might s s a s s real
ss estate s s appraiser s s select ssa s s sample s s of s s single-family s s homes s s that s s could s s be s s used s s as s s a
s s basis s s for s s developing s s an s s equation s s to s s predict ssappraised s s value s s from s s characteristics s s such
s s as s s age, s s size, s s number s s of s s bathrooms, s s and s s distance s s to s s the s s nearest ssschool, s s and s s so s s on?
Is s s the s s study s s enumerative s s or s s analytic?
ANS:
One s s could s s generate s s a s s simple s s random s s sample s s of s s all s s single s s family s s homes s s in s s the s s city
s s or s s a s s stratified s s random sssample s s by s s taking s s a s s simple s s random s s sample s s from s s each s s of s s the
s s 10 s s district s s neighborhoods. s s From s s each s s of s s the sshomes s s in s s the s s sample s s the s s necessary
s s variables s s would s s be s s collected. s s This s s would s s be s s an s s enumerative s s study ssbecause s s there s s exists
s s a s s finite, s s identifiable s s population s s of s s objects s s from s s which s s to s s sample.
, PTS: 1
4. An s s experiment s s was s s carried s s out s s to s s study s s how s s flow s s rate s s through s s a s s solenoid s s valve s s in
ss an s s automobile‘s sspollution-control s s system s s depended s s on s s three s s factors: armature s s lengths,
s s spring s s load, s s and s s bobbin s s depth. ssTwo s s different s s levels s s (low s s and s s high) s s of s s each s s factor
s s were s s chosen, s s and s s a s s single s s observation s s on s s flow s s was ssmade s s for s s each s s combination s s of
s s levels.
a. The s s resulting s s data s s set s s consisted s s of s s how s s many s s observations?
b. Is s s this s s an s s enumerative s s or s s analytic s s study? s s Explain s s your s s reasoning.
ANS:
a. Number s s observations s s equal s s 2 2 2=8
b. This s s could s s be s s called s s an s s analytic s s study s s because s s the s s data s s would ss be
s s collected s s on s s an s s existing ssprocess. s s There s s is s s no s s sampling s s frame.
PTS: 1
5. The s s accompanying s s data s s specific s s gravity s s values s s for s s various s s wood s s types s s used s s in s s construction s s .
.41 .41 .42 .42. .42 .42 .42 .43 .44
.54 .55 .58 .62 .66 .66 .67 .68 .75
.31 .35 .36 .36 .37 .38 .40 .40 .40
.45 .46 .46 .47 .48 .48 .48 .51 .54
Construct s s a s s stem-and-leaf s s display s s using s s repeated s s stems s s and s s comment s s on s s any s s interesting s s features
s s of s s the s s display.
ANS:
One s s method s s of s s denoting s s the s s pairs s s of s s stems s s having s s equal s s values s s is s s to s s denote s s the s s stem
s s by s s L, s s for s s ‗low‘ s s and ssthe s s second s s stem s s by s s H, s s for s s ‗high‘. Using s s this s s notation, s s the
s s stem-and-leaf s s display s s would s s appear s s as s s follows:
3L 1 stem:
s s tenths
3H 56678 leaf: hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H s s 5
The s s stem-and-leaf s s display s s on s s the s s previous s s page s s shows s s that s s .45 s s is s s a s s good s s representative
ssvalue s s for s s the s s data. s s In s s addition, s s the s s display s s is s s not s s symmetric s s and s s appears s s to s s be
s s positively s s skewed. The s s spread s s of s s the
s s data s s is
.75 s s - s s .31 s s = s s .44, s s which s s is s s .44/.45 s s = s s .978 s s or s s about s s 98% s s of s s the s s typical s s value s s of
s s .45. This s s constitutes s s a ssreasonably s s large s s amount s s of
s s variation s s in s s the s s data. The s s data s s value s s .75 s s is s s a s s possible s s outlier.
PTS: 1
6. Temperature s s transducers s s of s s a s s certain s s type s s are s s shipped s s in s s batches s s of s s 50. A
ss sample s s of s s 60 s s batches s s was ssselected, s s and s s the s s number s s of s s transducers s s in s s each s s batch
s s not s s conforming s s to s s design s s specifications s s was ssdetermined, s s resulting s s in s s the s s following
s s data:
0 4 2 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
s ss s s ss ss s
And The Sciences 8th Ed by Jay L. Devore.
ss ss ss ss ss ss ss ss ss
,
,Chapter 1 – Overview and Descriptive Statistics
ss ss ss ss ss ss
SHORT s s ANSWER
1. Give s s one s s possible s s sample s s of s s size s s 4 s s from s s each s s of s s the s s following s s populations:
a. All s s daily s s newspapers s s published s s in s s the s s United s s States
b. All s s companies s s listed s s on s s the s s New s s York s s Stock s s Exchange
c. All s s students s s at s s your s s college s s or s s university
d. All s s grade s s point s s averages s s of s s students s s at s s your s s college s s or s s university
ANS:
a. Houston s s Chronicle, s s Des s s Moines s s Register, s s Chicago s s Tribune, s s Washington s s Post
b. Capital s s One, s s Campbell s s Soup, s s Merrill s s Lynch, s s Pulitzer
c. John s s Anderson, s s Emily s s Black, s s Bill Carter, s s Kay s s Davis
d. 2.58. s s 2.96, s s 3.51, s s 3.69
PTS: 1
2. A s s Southern s s State s s University s s system s s consists s s of s s 23 s s campuses. s s An s s administrator s s wishes
ss to s s make s s an s s inference s s about s s the s s average s s distance s s between s s the s s hometowns s s of s s students
s s and s s their s s campuses. s s Describe s s and ssdiscuss s s several s s different s s sampling s s methods s s that s s might
s s be s s employed. s s Would s s this s s be s s an s s enumerative s s or s s an ssanalytic s s study? s s Explain s s your
s s reasoning.
ANS:
One s s could s s take s s a s s simple s s random s s sample s s of s s students s s from s s all s s students s s in s s the s s California
s s State s s University sssystem s s and s s ask s s each s s student s s in s s the s s sample s s to s s report s s the s s distance
s s from s s their s s hometown s s to s s campus.
Alternatively, s s the s s sample s s could s s be s s generated s s by s s taking s s a s s stratified s s random s s sample s s by
s s taking s s a s s simple ssrandom s s sample s s from s s each s s of s s the s s 23 s s campuses s s and s s again s s asking s s each
s s student s s in s s the s s sample s s to s s report s s the ssdistance s s from s s their s s hometown s s to s s campus.
Certain s s problems s s might s s arise s s with s s self s s reporting s s of s s distances, s s such s s as s s recording s s error s s or
s s poor s s recall. s s This ssstudy s s is s s enumerative s s because s s there s s exists s s a s s finite, s s identifiable
s s population s s of s s objects s s from s s which s s to s s sample.
PTS: 1
3. A s s Michigan s s city s s divides s s naturally s s into s s ten s s district s s neighborhoods. s s How s s might s s a s s real
ss estate s s appraiser s s select ssa s s sample s s of s s single-family s s homes s s that s s could s s be s s used s s as s s a
s s basis s s for s s developing s s an s s equation s s to s s predict ssappraised s s value s s from s s characteristics s s such
s s as s s age, s s size, s s number s s of s s bathrooms, s s and s s distance s s to s s the s s nearest ssschool, s s and s s so s s on?
Is s s the s s study s s enumerative s s or s s analytic?
ANS:
One s s could s s generate s s a s s simple s s random s s sample s s of s s all s s single s s family s s homes s s in s s the s s city
s s or s s a s s stratified s s random sssample s s by s s taking s s a s s simple s s random s s sample s s from s s each s s of s s the
s s 10 s s district s s neighborhoods. s s From s s each s s of s s the sshomes s s in s s the s s sample s s the s s necessary
s s variables s s would s s be s s collected. s s This s s would s s be s s an s s enumerative s s study ssbecause s s there s s exists
s s a s s finite, s s identifiable s s population s s of s s objects s s from s s which s s to s s sample.
, PTS: 1
4. An s s experiment s s was s s carried s s out s s to s s study s s how s s flow s s rate s s through s s a s s solenoid s s valve s s in
ss an s s automobile‘s sspollution-control s s system s s depended s s on s s three s s factors: armature s s lengths,
s s spring s s load, s s and s s bobbin s s depth. ssTwo s s different s s levels s s (low s s and s s high) s s of s s each s s factor
s s were s s chosen, s s and s s a s s single s s observation s s on s s flow s s was ssmade s s for s s each s s combination s s of
s s levels.
a. The s s resulting s s data s s set s s consisted s s of s s how s s many s s observations?
b. Is s s this s s an s s enumerative s s or s s analytic s s study? s s Explain s s your s s reasoning.
ANS:
a. Number s s observations s s equal s s 2 2 2=8
b. This s s could s s be s s called s s an s s analytic s s study s s because s s the s s data s s would ss be
s s collected s s on s s an s s existing ssprocess. s s There s s is s s no s s sampling s s frame.
PTS: 1
5. The s s accompanying s s data s s specific s s gravity s s values s s for s s various s s wood s s types s s used s s in s s construction s s .
.41 .41 .42 .42. .42 .42 .42 .43 .44
.54 .55 .58 .62 .66 .66 .67 .68 .75
.31 .35 .36 .36 .37 .38 .40 .40 .40
.45 .46 .46 .47 .48 .48 .48 .51 .54
Construct s s a s s stem-and-leaf s s display s s using s s repeated s s stems s s and s s comment s s on s s any s s interesting s s features
s s of s s the s s display.
ANS:
One s s method s s of s s denoting s s the s s pairs s s of s s stems s s having s s equal s s values s s is s s to s s denote s s the s s stem
s s by s s L, s s for s s ‗low‘ s s and ssthe s s second s s stem s s by s s H, s s for s s ‗high‘. Using s s this s s notation, s s the
s s stem-and-leaf s s display s s would s s appear s s as s s follows:
3L 1 stem:
s s tenths
3H 56678 leaf: hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H s s 5
The s s stem-and-leaf s s display s s on s s the s s previous s s page s s shows s s that s s .45 s s is s s a s s good s s representative
ssvalue s s for s s the s s data. s s In s s addition, s s the s s display s s is s s not s s symmetric s s and s s appears s s to s s be
s s positively s s skewed. The s s spread s s of s s the
s s data s s is
.75 s s - s s .31 s s = s s .44, s s which s s is s s .44/.45 s s = s s .978 s s or s s about s s 98% s s of s s the s s typical s s value s s of
s s .45. This s s constitutes s s a ssreasonably s s large s s amount s s of
s s variation s s in s s the s s data. The s s data s s value s s .75 s s is s s a s s possible s s outlier.
PTS: 1
6. Temperature s s transducers s s of s s a s s certain s s type s s are s s shipped s s in s s batches s s of s s 50. A
ss sample s s of s s 60 s s batches s s was ssselected, s s and s s the s s number s s of s s transducers s s in s s each s s batch
s s not s s conforming s s to s s design s s specifications s s was ssdetermined, s s resulting s s in s s the s s following
s s data:
0 4 2 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
