STATISTICS TEST 4 QUESTIONS WITH
CORRECT ANSWERS
For ssstudents sswho ssfirst ssenrolled ssin sstwo ssyear sspublic ssinstitutions ssin ssa ssrecent
sssemester, ssthe ssproportion sswho ssearned ssa ssbachelor's ssdegree sswithin sssix ssyears
sswas ss0.396. ssThe sspresident ssof ssa sscertain sscollege ssbelieves ssthat ssthe
ssproportion ssof ssstudents sswho ssenroll ssin ssher ssinstitution sshave ssa ss
higher
completion ssrate.
(a) ssState ssthe sshypotheses.
(b) ssWhich ssof ssthe ssfollowing ssis ssa ssType ssI ssError?
(c) ssWhich ssof ssthe ssfollowing ssis ssa ssType ssII ssError? ss- ssAnswer ss(a) ssThe
sshypothesis:
H0: ssp ss= ss.396
H1: ssp ss> ss.396
(b) ssA ssType ssI sserror ssis sscommitted sswhen ssthe ssnull sshypothesis ssis ssrejected
sswhen, ssin ssfact, ssit ssis sstrue sstherefore:
The sspresident ssrejects ssthe sshypothesis ssthat ssthe ssproportion ssof ssstudents sswho
ssearn ssa ssbachelor's ssdegree sswithin sssix ssyears ssis ss0.396,when, ssin ssfact, ssthe
ssproportion ssis ss0.396.
(c) ssA ssType ssII sserror ssis sscommitted sswhen ssthe ssnull sshypothesis ssis ssnot ssrejected
sswhen, ssin ssfact, ssthe ssalternative sshypothesis ssis sstrue sstherefore:
The sspresident ssfails ssto ssreject ssthe sshypothesis ssthat ssthe ssproportion ssof ssstudents
sswho ssearn ssa ssbachelor's ssdegree sswithin sssix ssyears ssis ss0.396, sswhen, ssin ssfact,
ssthe ssproportion ssis ss
greater ssthan ss0.396.
Three ssyears ssago, ssthe ssmean ssprice ssof ssan ssexisting sssingle-family sshome sswas ss
$243,765. ssA ssreal ssestate ssbroker ssbelieves ssthat ssexisting sshome ssprices ssin ssher
ssneighborhood ssare sslower.
(a) ssDetermine ssthe ssnull ssand ssalternative sshypotheses.
(b) ssExplain sswhat ssit sswould ssmean ssto ssmake ssa ssType ssI sserror.
(c) ssExplain sswhat ssit sswould ssmean ssto ssmake ssa ssType ssII sserror. ss- ssAnswer ss(a)
ssThe sshypothesis:
H0: ssμ ss= ss$243,765
H1: ssμ ss< ss$243,765
(b) ssThe ssbroker ssrejects ssthe sshypothesis ssthat ssthe ssmean ssprice ssis ss$243,765,
sswhen ssit ssis ssthe sstrue ssmean sscost.
, (c) ssThe ssbroker ssfails ssto ssreject ssthe sshypothesis ssthat ssthe ssmean ssprice ssis ss
$243,765, sswhen ssthe sstrue ssmean ssprice ssis ssless ssthan ss$243,765
The ssstandard ssdeviation ssin ssthe sspressure ssrequired ssto ssopen ssa sscertain ssvalve
ssis ssknown ssto ssbe ssσ=1.3 sspsi. ssDue ssto sschanges ssin ssthe ssmanufacturing
ssprocess, ssthe ssquality-control ssmanager ssfeels ssthat ssthe sspressure ssvariability sshas
ssbeen ssreduced.
(a) ssDetermine ssthe ssnull ssand ssalternative sshypotheses.
(b) ssExplain sswhat ssit sswould ssmean ssto ssmake ssa ssType ssI sserror.
(c) ssExplain sswhat ssit sswould ssmean ssto ssmake ssa ssType ssII sserror. ss- ssAnswer ss(a)
ssThe sshypothesis:
σ ss= ss1.3
σ ss< ss1.3 ss
(b) ssThe ssmanager ssrejects ssthe sshypothesis ssthat ssthe sspressure ssvariability ssis ss1.3,
sswhen ssit ssis ssthe sstrue sspressure ssvariability.
(c) ssThe ssmanager ssfails ssto ssreject ssthe sshypothesis ssthat ssthe sspressure ssvariability
ssis ss1.3, sswhen ssthe sstrue sspressure ssvariability ssis ssless ssthan ss1.3.
A sscan ssof sssoda ssis sslabeled ssas sscontaining ss16 ssfluid ssounces. ssThe ssquality
sscontrol ssmanager sswants ssto ssverify ssthat ssthe ssfilling ssmachine ssis ssnot ssover-filling
ssthe sscans. ssComplete ssparts ss(a) ssthrough ss(d) ssbelow.
(a) ssDetermine ssthe ssnull ssand ssalternative sshypotheses ssthat sswould ssbe ssused ssto
ssdetermine ssif ssthe ssfilling ssmachine ssis sscalibrated sscorrectly
(b) ssThe ssquality sscontrol ssmanager ssobtains ssa sssample ssof ss79 sscans ssand
ssmeasures ssthe sscontents. ssThe sssample ssevidence ssleads ssthe ssmanager ssto
ssreject ssthe ssnull sshypothesis. ssWrite ssa ssconclusion ssfor ssthis sshypothesis sstest...
There ss??? sssufficient ssevidence ssto ssconclude ssthat ssthe ssmachine ssis ssout ssof
sscalibration.
(c) ssA ss??? sshas ssbeen ssmade sssince ssthe sssample ssevidence ssled ssthe ssquality
sscontrol ssmanager ssto ss??? ssthe ssnull sshypothesis, sswhen ssthe ss??? ssis sstrue.
(d) ssManagement sshas ssinformed ssthe ssquality sscontrol ssdepartment ssthat ssit ssdoes
ssnot sswant ssto ssshut ssdown ssthe ssfilling ssmachine ssunless ssthe ssevidence ssis
ssoverwhelming ssthat ssthe ssmachine ssis ssout ssof sscalibrat ss- ssAnswer ss(a) ssThe
sshypothesis:
H0: ssμ ss= ss16
H1: ssμ ss> ss16
(b) ssis
note: sswhen ssthe ssnull sshypothesis ssis ssrejected, ssthe ssalternative sshypothesis ssis
sssupported. ssThis ssmeans ssthat ssthere ssis sssufficient ssevidence ssto ssconclude ssthat
ssthe ssmachine ssis ssout ssof sscontrol. ss
(c) ssType ssI sserror, ssreject, ssnull sshypothesis
A ssType ssI sserror ssis sscommitted sswhen ssthe ssnull sshypothesis ssis ssrejected sswhen,
ssin ssfact, ssit ssis sstrue. ssA ssType ssII sserror ssis sscommitted sswhen ssthe ssnull
sshypothesis ssis ssnot ssrejected sswhen, ssin ssfact, ssthe ssalternative sshypothesis ssis
sstrue. ssA ssType ssI sserror sshas ssbeen ssmade sssince ssthe sssample ssevidence ssled
CORRECT ANSWERS
For ssstudents sswho ssfirst ssenrolled ssin sstwo ssyear sspublic ssinstitutions ssin ssa ssrecent
sssemester, ssthe ssproportion sswho ssearned ssa ssbachelor's ssdegree sswithin sssix ssyears
sswas ss0.396. ssThe sspresident ssof ssa sscertain sscollege ssbelieves ssthat ssthe
ssproportion ssof ssstudents sswho ssenroll ssin ssher ssinstitution sshave ssa ss
higher
completion ssrate.
(a) ssState ssthe sshypotheses.
(b) ssWhich ssof ssthe ssfollowing ssis ssa ssType ssI ssError?
(c) ssWhich ssof ssthe ssfollowing ssis ssa ssType ssII ssError? ss- ssAnswer ss(a) ssThe
sshypothesis:
H0: ssp ss= ss.396
H1: ssp ss> ss.396
(b) ssA ssType ssI sserror ssis sscommitted sswhen ssthe ssnull sshypothesis ssis ssrejected
sswhen, ssin ssfact, ssit ssis sstrue sstherefore:
The sspresident ssrejects ssthe sshypothesis ssthat ssthe ssproportion ssof ssstudents sswho
ssearn ssa ssbachelor's ssdegree sswithin sssix ssyears ssis ss0.396,when, ssin ssfact, ssthe
ssproportion ssis ss0.396.
(c) ssA ssType ssII sserror ssis sscommitted sswhen ssthe ssnull sshypothesis ssis ssnot ssrejected
sswhen, ssin ssfact, ssthe ssalternative sshypothesis ssis sstrue sstherefore:
The sspresident ssfails ssto ssreject ssthe sshypothesis ssthat ssthe ssproportion ssof ssstudents
sswho ssearn ssa ssbachelor's ssdegree sswithin sssix ssyears ssis ss0.396, sswhen, ssin ssfact,
ssthe ssproportion ssis ss
greater ssthan ss0.396.
Three ssyears ssago, ssthe ssmean ssprice ssof ssan ssexisting sssingle-family sshome sswas ss
$243,765. ssA ssreal ssestate ssbroker ssbelieves ssthat ssexisting sshome ssprices ssin ssher
ssneighborhood ssare sslower.
(a) ssDetermine ssthe ssnull ssand ssalternative sshypotheses.
(b) ssExplain sswhat ssit sswould ssmean ssto ssmake ssa ssType ssI sserror.
(c) ssExplain sswhat ssit sswould ssmean ssto ssmake ssa ssType ssII sserror. ss- ssAnswer ss(a)
ssThe sshypothesis:
H0: ssμ ss= ss$243,765
H1: ssμ ss< ss$243,765
(b) ssThe ssbroker ssrejects ssthe sshypothesis ssthat ssthe ssmean ssprice ssis ss$243,765,
sswhen ssit ssis ssthe sstrue ssmean sscost.
, (c) ssThe ssbroker ssfails ssto ssreject ssthe sshypothesis ssthat ssthe ssmean ssprice ssis ss
$243,765, sswhen ssthe sstrue ssmean ssprice ssis ssless ssthan ss$243,765
The ssstandard ssdeviation ssin ssthe sspressure ssrequired ssto ssopen ssa sscertain ssvalve
ssis ssknown ssto ssbe ssσ=1.3 sspsi. ssDue ssto sschanges ssin ssthe ssmanufacturing
ssprocess, ssthe ssquality-control ssmanager ssfeels ssthat ssthe sspressure ssvariability sshas
ssbeen ssreduced.
(a) ssDetermine ssthe ssnull ssand ssalternative sshypotheses.
(b) ssExplain sswhat ssit sswould ssmean ssto ssmake ssa ssType ssI sserror.
(c) ssExplain sswhat ssit sswould ssmean ssto ssmake ssa ssType ssII sserror. ss- ssAnswer ss(a)
ssThe sshypothesis:
σ ss= ss1.3
σ ss< ss1.3 ss
(b) ssThe ssmanager ssrejects ssthe sshypothesis ssthat ssthe sspressure ssvariability ssis ss1.3,
sswhen ssit ssis ssthe sstrue sspressure ssvariability.
(c) ssThe ssmanager ssfails ssto ssreject ssthe sshypothesis ssthat ssthe sspressure ssvariability
ssis ss1.3, sswhen ssthe sstrue sspressure ssvariability ssis ssless ssthan ss1.3.
A sscan ssof sssoda ssis sslabeled ssas sscontaining ss16 ssfluid ssounces. ssThe ssquality
sscontrol ssmanager sswants ssto ssverify ssthat ssthe ssfilling ssmachine ssis ssnot ssover-filling
ssthe sscans. ssComplete ssparts ss(a) ssthrough ss(d) ssbelow.
(a) ssDetermine ssthe ssnull ssand ssalternative sshypotheses ssthat sswould ssbe ssused ssto
ssdetermine ssif ssthe ssfilling ssmachine ssis sscalibrated sscorrectly
(b) ssThe ssquality sscontrol ssmanager ssobtains ssa sssample ssof ss79 sscans ssand
ssmeasures ssthe sscontents. ssThe sssample ssevidence ssleads ssthe ssmanager ssto
ssreject ssthe ssnull sshypothesis. ssWrite ssa ssconclusion ssfor ssthis sshypothesis sstest...
There ss??? sssufficient ssevidence ssto ssconclude ssthat ssthe ssmachine ssis ssout ssof
sscalibration.
(c) ssA ss??? sshas ssbeen ssmade sssince ssthe sssample ssevidence ssled ssthe ssquality
sscontrol ssmanager ssto ss??? ssthe ssnull sshypothesis, sswhen ssthe ss??? ssis sstrue.
(d) ssManagement sshas ssinformed ssthe ssquality sscontrol ssdepartment ssthat ssit ssdoes
ssnot sswant ssto ssshut ssdown ssthe ssfilling ssmachine ssunless ssthe ssevidence ssis
ssoverwhelming ssthat ssthe ssmachine ssis ssout ssof sscalibrat ss- ssAnswer ss(a) ssThe
sshypothesis:
H0: ssμ ss= ss16
H1: ssμ ss> ss16
(b) ssis
note: sswhen ssthe ssnull sshypothesis ssis ssrejected, ssthe ssalternative sshypothesis ssis
sssupported. ssThis ssmeans ssthat ssthere ssis sssufficient ssevidence ssto ssconclude ssthat
ssthe ssmachine ssis ssout ssof sscontrol. ss
(c) ssType ssI sserror, ssreject, ssnull sshypothesis
A ssType ssI sserror ssis sscommitted sswhen ssthe ssnull sshypothesis ssis ssrejected sswhen,
ssin ssfact, ssit ssis sstrue. ssA ssType ssII sserror ssis sscommitted sswhen ssthe ssnull
sshypothesis ssis ssnot ssrejected sswhen, ssin ssfact, ssthe ssalternative sshypothesis ssis
sstrue. ssA ssType ssI sserror sshas ssbeen ssmade sssince ssthe sssample ssevidence ssled
