Point Estimation - Wilkes Universitymathcs.wilkes.edu/~rpryor/mth150/CI.pdfEstimating the difference...
Transcript of Point Estimation - Wilkes Universitymathcs.wilkes.edu/~rpryor/mth150/CI.pdfEstimating the difference...
Point Estimation
mth_%&'
Data Distributions vs Probability Distributions
Confidence Interval of the mean
Taking Samples
!"#$!%!&!'!&(&!"!$!$#$()!!!!#(!'!"!!('('#!('!"(!!"!(#!!"!!!#
%,'),'*,'+,'&,',,'-,'.,'/,'
Population Size: /01
MU : /4.4/
SIGMA : 0./9990
VAR : /<.<4<9
Number of intervals:
D1/1
-> /4
-> D/
.4
/4 ->np ->
1.0EEE/F
1.9GE1<G
//
D11
E1
)))%)%))))))))
Number of Samples:
Sample. Size:
Mean of Sampling Distribution:
Standard Deviation ofSampling Distribution:
Standard Error: (Calculated)
S A M P L E
Sampling Distribution (Means)
G
#'.)"("#"#.')!%)%").!+)&#%"+.#+&+&"!.&(%"$%"!.")+%&%#&.'$'+%%"'.('##'%"!.%'+"&%"(."#&%+"".'&"+#"#.$(##(%"+.#$!+'%"(.))"'&"#.$+'+#%$.#%+"+"'.!++"%$."("%!%"$.''!"'"$.)"(!!").%!$#)"$.)!$%+%""."!!&"%"!.#$'%#%(.''###%!.%)'+&").&"%+&%#".+((#)%#&.)%'&'%""."%)$+%
%,'),'*,'+,'&,',,%-,%.,)/,)
Population Size: /01
MU : G9.111D0/
SIGMA : G.FGE4F/
VAR : /G.GE90E0
Number of intervals:
D1/1
-> G0
-> 0
.4
/4 ->np ->
D.D19GFG
<.G9/10<
/9./9D11D
D111
/1
)/.&**&+,+*.-&%*%%%,.*/'%'+),.,+/&*-%..'-*)')),.%--'++%-..+%'-
Number of Samples:
Sample. Size:
Mean of Sampling Distribution:
Standard Deviation ofSampling Distribution:
Standard Error: (Calculated)
S A M P L E
Sampling Distribution (Variances)
G
#'.)"("#"#.')!%)%").!+)&#%"+.#+&+&"!.&(%"$%"!.")+%&%#&.'$'+%%"'.('##'%"!.%'+"&%"(."#&%+"".'&"+#"#.$(##(%"+.#$!+'%"(.))"'&"#.$+'+#%$.#%+"+"'.!++"%$."("%!%"$.''!"'"$.)"(!!").%!$#)"$.)!$%+%""."!!&"%"!.#$'%#%(.''###%!.%)'+&").&"%+&%#".+((#)%#&.)%'&'%""."%)$+%
%,-),+/*,%*/+,)%&&,)%/,,%/'-,%%&.,+%/,)%
Population Size: /01
MU : G9.111D0/
SIGMA : G.FGE4F/
VAR : /G.GE90E0
Number of intervals:
D1/1
-> G0
-> 0
.4
/4 ->np ->
/./D/FEE
D.9GF0/E
G.F9D<F9
D111
0
,.&,%-*.-.//)'.,*../*.%*%.+,+'*-.+-/,.+.)-)&).+.*,+%')
Number of Samples:
Sample. Size:
Mean of Sampling Distribution:
Standard Deviation ofSampling Distribution:
Standard Error: (Calculated)
S A M P L E
Sampling Distribution (Standard Deviations)
G
$.(&&#$+$.)&&%'%$.#)"''%$.!$$&++$.%$&&!'$.!))%)'$."+&&'($.$&'!+$."%!##!$.$++"(+$.$"%(#%$.(!+#%#$.)+$'$.#""&+)$.!%($!'$.!!%%!&$.$(#%''$.((%&'%$.$%"!''$.('!++($.#&+"+#$.$')%%)$.$(%$+'$.$#'&&)$.")&&&%$.$"($('$.$$'+'%$.$&"!#+$.$)#%)%$.(%)#)!
,%,%,%,),),),%,%,%,%,%,%,%,%,),%,*,%,%,%,),),%,%,),),%,%,%,%,%,%,%,),%,%,*,),%,),%,%,%,%,%,%,%,%,%,%,%,),%,%,%,),%,),%,%,%,%,%,%,%,%,%,%,%,%,),%,+,),%,%,%,%,%,*,),*,%,%,%,%,%,%,),),%,),%,%,%,%,),),%,%,%,%,%,%,),+,%,%,%,),%,%,%,%,%,%,%,%,%,%,%,%,%,%,%,%,%,%,%,%,%,),%,%,%,%,%,%,%,%,%,%,%,),%,%,%,%,),),%,%,%,%,%,),%,),),),%,%,%,%,),),%,%,),%,%,),%,%,%,%,%,%,%,%,),*,*,%,%,%,%,%,%,%,%,%,%,%,*,),%,%,),),%,%,,,),%,*,%,%,%,%,%,%,%,%,%,+,%,%,*,),%,+,),%,*,%,%,%,%,%,),%,*,%,%,%,%,%,),%,%,%,),%,%,),%,%,%,),%,%,%,%,*,),%,%,%,%,%,%,%,%,%,%,%,%,%,%,%,),),%,%,%,*,%,%,),%,%,*,%,+,),*,%,%,%,%,%,),),%,%,%,%,%,%,),%,*,%,%,%,%,%,%,%,%,%,%,%,%,%,%,%,%,),%,%,%,%,%,%,%,%,%,%,&,%,%,%,%,%,%,),%,%,%,%,%,%,),%,%,%,%,%,%,%,%,%,%,%,),%,),),%,%,%,%,%,%,%,),%,%,%,%,%,),),%,),%,%,%,%,%,%,%,%,),),%,%,),%,&,%,%,%,),*,%,%,),*,%,%,*,%,%,%,%,%,%,),%,),%,&,%,%,%,%,%,%,%,*,%,%,%,%,%,%,),%,%,%,%,%,),%,*,%,%,%,%,%,),),%,%,*,%,%,%,%,%,%,),),%,%,),%,%,%,),%,),%,%,%,%,*,%,%,%,%,%,),%,%,),%,%,),),%,%,),%,%,%,%,%,%,),%,%,%,%,),%,),%,%,%,%,%,%,%,%,),%,),%,%,%,%,*,%,%,*,),%,%,),%,%,%,),%,%,%,%,),%,%,%,%,%,%,%,%,%,%,%,),%,),),%,%,%,%,%,%,%,),%,),%,%,),),%,%,%,%,),%,%,%,%,%,%,%,%,%,%,%,%,%,%,),),%,),%,%,%,%,%,%,*,),%,),%,%,%,%,%,),%,),%,%,%,%,%,),%,%,%,),%,%,),%,%,%,*,*,+,%,),),%,%,%,%,),%,%,%,%,%,%,),%,%,),%,%,*,%,+,%,),%,%,%,%,%,%,),%,%,%,%,%,%,*,%,),),%,),*,*,+,),%,%,*,%,%,%,%,%,%,%,),%,%,),%,),%,%,),%,%,%,%,%,%,%,%,%,%,%,%,%,),),%,%,),%,%,%,%,*,%,),%,%,),%,),%,%,%,+,%,%,%,*,%,%,),%,%,%,%,%,%,%,%,%,%,%,%,),%,%,%,%,%,%),'),'*,'+,'&,',,'-,'.,'/,'
Population Size: /11
MU : 1./GFG/F
SIGMA : 1.//<F4/
VAR : 1.10DF04
Number of intervals:
D1/1
-> D4
-> D/
.<
/0 ->np ->
1.D1DF4G
1./D94<F
1.G/</90
D111
0
'.%.&).,'.,-+%*.'.%.-//.'.)'%*'+'.))/-.-'.+*/+&-'.)++-%&
Number of Samples:
Sample. Size:
Mean of Sampling Distribution:
Standard Deviation ofSampling Distribution:
Standard Error: (Calculated)
S A M P L E
Sampling Distribution (Ranges)
RANGE : D.4D9F9F
G
!"#$!%!&!'!&(&!"!$!$#$()!!!!#(!'!"!!('('#!('!"(!!"!(#!!"!!!#
%,'),'*,'+,'&,',,'-,'.,'/,'
Population Size: /01
MU : /4.4/
SIGMA : 0./9990
VAR : /<.<4<9
Number of intervals:
D1/1
-> /4
-> D/
.4
/4 ->np ->
1.0EEE/F
1.9GE1<G
//
D11
E1
)))%)%))))))))
Number of Samples:
Sample. Size:
Mean of Sampling Distribution:
Standard Deviation ofSampling Distribution:
Standard Error: (Calculated)
S A M P L E
Sampling Distribution (Medians)
G
MEDIAN: /<.<4<9
#+.%(("'%+."&#$)+"".$'"&+'%$.&"#"##.&%$$$'%+.%!(#!"#).$+!!#!!'."'$)#!#&.%)$+$"#(.#'%!'"%%.%%!$(!"+.+&!)(!%+.&&#"$"%".')'%"'"&.)(("'"&.(#+'!"#+."(&"''##.$''%(+#&.'"'!#$."'"+"'!'.+""!&!"(.#)"!%!"'.#"'((!#!.#'$#&+%(.)%'')!"".%#$(&!"+.#$$#+%+.)#$#%!().#%&%$""%.!%)#+'
%,'),'*,'+,'&,',,'-,'.,'/,'
Population Size: /111
MU : G4.DD4EF9
SIGMA : D/.19D4GG
VAR : DG0.G<91DF
Number of intervals:
D1/1
-> G4
-> D/
.4
/4 ->np ->
1.F0/
0.4/G<1E
G/.00F
D111
0
+'*.+.*.+++'+%
Number of Samples:
Sample. Size:
Mean of Sampling Distribution:
Standard Deviation ofSampling Distribution:
Standard Error: (Calculated)
S A M P L E
0.4F4FF<
F1%F0%FE%FF%
G
-D.F9 D.F91
Normality ?
Estimating the mean
-D.9G0/DD D.9G0/DD
R E S E T
z t
( using standard normal and Student's t )
Student's t Distribution
->
->
Estimating the mean( using standard normal and Student's t )
Estimating the mean
-D.F914F0 D.F914F0
R E S E T
z
( using population proportions )
Estimating the variance
1.00G4 D0.1E94
->n
R E S E T
Chi-Square Distribution
->
->
Calculating the sample size
R E S E T
/.4/9<E0
Estimating the difference between two means
-D.<G9/F< D.<G9/F<
z t
( Using standard normal and Student's t )
R E S E T
equalunequal
Estimating the difference between two proportions
z
( Using standard normal distrinution )
R E S E T
Estimating the difference between two means
-/.DG04/< /.DG04/<
t
( interactive or "matched" pairs )
R E S E T
!!'!$(()&'&'!("!)!(%!&!(++!("()"(!"
("'(#!(%%("$(("(!!(!!(&#((!($"(('(+$($'
'$+&!"-%(-#!!$-%$-"(-!$+!&+("(+
Clear Data Tables
!."()"$((.!%"%&&-(."$!#&!$.$%'$%!-$.")&")!-(.(+'%'+$.)""!$'$.'&%(%)-$.$#+$#&(.&%#'&-(.$#)!$%-(.#!'%$)-$.#'&('%$.(%%'!#(.+()$))-$.!!%&!#$."+)+)'(.$!%'''(.+"!"('-!.$)+))$.+%"+#&(.")"&('(.(%))(&$.$'$('$.%))+#$."'&)$#-!.")%'#%-(.!%$)%!#.+!%)%+$.'"""!(
-,./,//+/-+./,.//)-*./*/.&--*./%'&&+-*.-)*.-)-*.-''/&*-*.&,%/---*.*/,+%/-*.).+*'%
Population Size: 011
MU : 1.1140DE
SIGMA : D.G/140F
VAR : /.1D<GDF
Number of intervals:
D1/1
-> /4
-> D/
.4
/4 ->np ->
1.940/1G
1.4F4E1D
1.1EF
D111
0
'''''%'
Number of Samples:
Sample. Size:
Mean of Sampling Distribution:
Standard Deviation ofSampling Distribution:
Standard Error: (Calculated)
S A M P L E
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