hypothesis testing-1 (1)
Post on 07-Nov-2015
218 Views
Preview:
TRANSCRIPT
-
HYPOTHESIS
TESTING
INSURANCE CLAIM EXAMPLE
!" #
EMPLOYEE ABSENTEEISM
EXAMPLE
$ # %
&
&
#
'(#
"
HYPOTHESIS TESTING
We estimate parameters by using
Are they correct ? ?
-
DIPLOMA PROGRAM EXAMPLE
) * # +" ,
(
-
+
PLANT NURSERY EXAMPLE
#
+"&
.+#
$+'#
$"#
HYPOTHESIS TESTING
We made certain claims
We garanteed certain things
Are they correct ? ?
NULL HYPOTHESIS
Testing a Belief
Testing a Claim
Claim / Belief
Null Hypotheses -
-
EXAMPLES
HHHH0 0 0 0 : = 100 #+
HHHH0 0 0 0 : p = 0.5 #"
HHHH0 0 0 0 : 75 #
/!"
ALTERNATIVE HYPOTHESIS
What will happen
if
null hypothesis
is rejected
Alternative Hypotheses -
EXAMPLES #+
HHHH0 0 0 0 : = 100 HHHH1 1 1 1 : 100
#"
HHHH0 0 0 0 : p = 0.5
HHHH1 1 1 1 : p 0.5
COMPOSITE HYPOTHESIS #+
HHHH0 0 0 0 : 100 HHHH1 1 1 1 :
-
HOW TO TEST
POPULATION
SAMPLE
SAMPLE
QUANTITY
TESTING FOR POPULATION MEAN
.0001
23452.00
HHHH0 0 0 0 : = 100 HHHH1111 : 100
).105-
Reject HHHH0 0 0 0 if Z is very LARGE or very SMALL
P ( P ( P ( P ( ---- 1.96 < Z < 1.96 ) = 0.95 = 95%1.96 < Z < 1.96 ) = 0.95 = 95%1.96 < Z < 1.96 ) = 0.95 = 95%1.96 < Z < 1.96 ) = 0.95 = 95%
P ( Z < P ( Z < P ( Z < P ( Z < ----1.96 or Z > 1.96 ) = 0.05 = 5%1.96 or Z > 1.96 ) = 0.05 = 5%1.96 or Z > 1.96 ) = 0.05 = 5%1.96 or Z > 1.96 ) = 0.05 = 5%
If Z > 1.96 or Z < If Z > 1.96 or Z < If Z > 1.96 or Z < If Z > 1.96 or Z < ----1.96 1.96 1.96 1.96
we reject Hwe reject Hwe reject Hwe reject H0 0 0 0 with 95% confidence with 95% confidence with 95% confidence with 95% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
TESTING FOR POPULATION MEAN
.0001
23452.00
HHHH0 0 0 0 : 100 HHHH1111 :
-
P ( Z < 1.64 ) = 0.95 = 95%P ( Z < 1.64 ) = 0.95 = 95%P ( Z < 1.64 ) = 0.95 = 95%P ( Z < 1.64 ) = 0.95 = 95%
P ( Z > P ( Z > P ( Z > P ( Z > ----1.64 ) = 0.95 = 95%1.64 ) = 0.95 = 95%1.64 ) = 0.95 = 95%1.64 ) = 0.95 = 95%
P ( Z < P ( Z < P ( Z < P ( Z < ----1.64 ) = 0.05 = 5%1.64 ) = 0.05 = 5%1.64 ) = 0.05 = 5%1.64 ) = 0.05 = 5%
If Z < If Z < If Z < If Z < ----1.64 1.64 1.64 1.64
we reject Hwe reject Hwe reject Hwe reject H0 0 0 0 with 95% confidence with 95% confidence with 95% confidence with 95% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
TESTING FOR POPULATION MEAN
.0001
23452.00
HHHH0 0 0 0 : 100 HHHH1111 : >>>> 100
).105-
Reject HHHH0 0 0 0 if Z is very LARGE
P ( Z < 1.64 ) = 0.95 = 95%P ( Z < 1.64 ) = 0.95 = 95%P ( Z < 1.64 ) = 0.95 = 95%P ( Z < 1.64 ) = 0.95 = 95%
P ( Z > 1.64 ) = 0.05 = 5%P ( Z > 1.64 ) = 0.05 = 5%P ( Z > 1.64 ) = 0.05 = 5%P ( Z > 1.64 ) = 0.05 = 5%
If Z > 1.64 If Z > 1.64 If Z > 1.64 If Z > 1.64
we reject Hwe reject Hwe reject Hwe reject H0 0 0 0 with 95% confidence with 95% confidence with 95% confidence with 95% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
DAILY MEAL EXAMPLE
'"#
#
# &
% #
#
'%"#
#"6
-
X = SPENDING FOR DAILY MEALS
23452.00
HHHH0 0 0 0 : = 250 HHHH1111 : 250
N = 36 =265 = 40
.00010
X = SPENDING FOR DAILY MEALS
!"#
$ %&'("#
Z > 1.96Z > 1.96Z > 1.96Z > 1.96
we reject Hwe reject Hwe reject Hwe reject H0 0 0 0 with 95% confidence with 95% confidence with 95% confidence with 95% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
2.25 2.25 2.25 2.25
AVERAGE SPENDING HAS CHANGED.AVERAGE SPENDING HAS CHANGED.AVERAGE SPENDING HAS CHANGED.AVERAGE SPENDING HAS CHANGED.
----2.57 < Z < 2.572.57 < Z < 2.572.57 < Z < 2.572.57 < Z < 2.57
we cannot reject Hwe cannot reject Hwe cannot reject Hwe cannot reject H0 0 0 0 with 99% confidence with 99% confidence with 99% confidence with 99% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
) )
2.25 2.25 2.25 2.25
CANNOT SAY AVERAGE SPENDING HAS CANNOT SAY AVERAGE SPENDING HAS CANNOT SAY AVERAGE SPENDING HAS CANNOT SAY AVERAGE SPENDING HAS
CHANGED WITH 99% CONFIDENCE.CHANGED WITH 99% CONFIDENCE.CHANGED WITH 99% CONFIDENCE.CHANGED WITH 99% CONFIDENCE.
-
PRODUCTIVITY IMPROVEMENT
EXAMPLE #
& '" #
, # /
,#+* /
, ' # +% ##
,
X = TIME REQUIRED TO DO A JOB
23452.00
HHHH0 0 0 0 : 20 HHHH1111 : Z > Z > Z > ----0.6250.6250.6250.625
we cannot reject Hwe cannot reject Hwe cannot reject Hwe cannot reject H0 0 0 0 with 95% confidence with 95% confidence with 95% confidence with 95% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
----0.625 0.625 0.625 0.625
WE CANNOT SAY THAT THE TRAINING HAS WE CANNOT SAY THAT THE TRAINING HAS WE CANNOT SAY THAT THE TRAINING HAS WE CANNOT SAY THAT THE TRAINING HAS
REDUCED THE TIME REQUIRED TO THE JOB REDUCED THE TIME REQUIRED TO THE JOB REDUCED THE TIME REQUIRED TO THE JOB REDUCED THE TIME REQUIRED TO THE JOB
SIGNIFICANTLY.SIGNIFICANTLY.SIGNIFICANTLY.SIGNIFICANTLY.
-
ELECTRIC RESISTORS EXAMPLE
# # !"
2#& # ' #
#
+6
"
X = CURRENT PASSES THROUGH A
RESISTOR
23452.00
HHHH0 0 0 0 : 0.75 HHHH1111 : >>>> 0.75
N = 32 =0.9 = 0.5
.00010
X = CURRENT PASSES THROUGH A RESISTOR
!"#
$ %&'("#
Z < 1.28Z < 1.28Z < 1.28Z < 1.28
we cannot reject Hwe cannot reject Hwe cannot reject Hwe cannot reject H0 0 0 0 with 90% confidence with 90% confidence with 90% confidence with 90% confidence
(at 10% level of significance)(at 10% level of significance)(at 10% level of significance)(at 10% level of significance)
*
1.2 1.2 1.2 1.2
WE CANNOT SAY THAT MORE THAN 0.75 WE CANNOT SAY THAT MORE THAN 0.75 WE CANNOT SAY THAT MORE THAN 0.75 WE CANNOT SAY THAT MORE THAN 0.75
AMPERES PASSES THROUGH A RESISTOR.AMPERES PASSES THROUGH A RESISTOR.AMPERES PASSES THROUGH A RESISTOR.AMPERES PASSES THROUGH A RESISTOR.
-
UNKNOWN POPULATION VARIANCE
"+",,,
-%
%"-
UNKNOWN POPULATION VARIANCE
(""+%"+./
&"(("-
LIGHT BULBS EXAMPLE
%7!"8+' # #9:
%! ! "" " ! !* *" !" *" ** %'" !"
"6
X = LIFE TIME OF A LIGHT BULB
23452.00
HHHH0 0 0 0 : 750 HHHH1111 :
-
X = LIFE TIME OF A LIGHT BULB
!"#
$ %&'("#
*
Z > Z > Z > Z > ----1.791.791.791.79
we cannot reject Hwe cannot reject Hwe cannot reject Hwe cannot reject H0 0 0 0 with 95% confidence with 95% confidence with 95% confidence with 95% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
)
----0.89 0.89 0.89 0.89
WE CANNOT SAY THAT THE LIFE TIME OF WE CANNOT SAY THAT THE LIFE TIME OF WE CANNOT SAY THAT THE LIFE TIME OF WE CANNOT SAY THAT THE LIFE TIME OF
LIGHT BULB IS SIGNIFICANTLY LESS THAN LIGHT BULB IS SIGNIFICANTLY LESS THAN LIGHT BULB IS SIGNIFICANTLY LESS THAN LIGHT BULB IS SIGNIFICANTLY LESS THAN
750 HOURS750 HOURS750 HOURS750 HOURS
---- 0.196 > 0.196 > 0.196 > 0.196 > ---- 0.05 0.05 0.05 0.05
we cannot reject Hwe cannot reject Hwe cannot reject Hwe cannot reject H0 0 0 0 with 95% confidence with 95% confidence with 95% confidence with 95% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
*
WE CANNOT SAY THAT THE LIFE TIME OF WE CANNOT SAY THAT THE LIFE TIME OF WE CANNOT SAY THAT THE LIFE TIME OF WE CANNOT SAY THAT THE LIFE TIME OF
LIGHT BULB IS SIGNIFICANTLY LESS THAN LIGHT BULB IS SIGNIFICANTLY LESS THAN LIGHT BULB IS SIGNIFICANTLY LESS THAN LIGHT BULB IS SIGNIFICANTLY LESS THAN
750 HOURS750 HOURS750 HOURS750 HOURS
MICROSOFT EXCEL OUTPUT 0
1 !" 23)
4'"(&(
-!5
-!6 )*7777777
-!0'" 7*)
-"
""(6 77*
0&"(8"-
*))*7
4"+
4"+9 )***
!9 )
0"": !"
-
MICROSOFT EXCEL INSTRUCTIONS
1. Click on PHStat tab
2. Select One Sample Test, t-test for Mean, Sigma
unknown
3. Enter Hypothesized Mean
4. Check Sample Statistics unknown
5. Check Test Statistics > Lower Tail Test
MINITAB OUTPUT
MINITAB INSTRUCTIONS POLLUTION COUNT EXAMPLE
'"-" " +
% % (" '& " ( '& !"" " " "
; " " % "( + !"
("'&!"""+""'!""(
"' (""+&+"%
) * 7
*
) 7
+%("'&
-
X = POLLUTION COUNT FOR THE CITY
23452.00
HHHH0 0 0 0 : 150 HHHH1111 : >>>> 150
N = 20 =150.7 S = 5.25
.00010
X = LIFE TIME OF A LIGHT BULB
!"#
/
$ %&'("#
.
./
Z < 1.729Z < 1.729Z < 1.729Z < 1.729
we cannot reject Hwe cannot reject Hwe cannot reject Hwe cannot reject H0 0 0 0 with 95% confidence with 95% confidence with 95% confidence with 95% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
)
0.59 0.59 0.59 0.59
WE CANNOT SAY THAT THE AREA IS NOT WE CANNOT SAY THAT THE AREA IS NOT WE CANNOT SAY THAT THE AREA IS NOT WE CANNOT SAY THAT THE AREA IS NOT
SUITABLE FOR LIVINGSUITABLE FOR LIVINGSUITABLE FOR LIVINGSUITABLE FOR LIVING
MICROSOFT EXCEL OUTPUT
0
1 !"
-
VEHICLE PURCHASING EXAMPLE
##2
'&
-#
# &
& #
& +* 0 9 :
####
' '" + '' ' ' +* ' ''
' ' '+ '' +* + ' '+ '
"6#
X = PRICE OF THE VEHICLE
23452.00
HHHH0 0 0 0 : = 2.4= 2.4= 2.4= 2.4 HHHH1111 : : : : 2.4
N = 18 =2.14 S = 0.22
.00010
X = PRICE OF THE VEHICLE
!"#
.
/
$ %&'("#
..
./
Z < Z < Z < Z < ---- 2.112.112.112.11
we reject Hwe reject Hwe reject Hwe reject H0 0 0 0 with 95% confidence with 95% confidence with 95% confidence with 95% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
---- 5.10 5.10 5.10 5.10
PRICE OF THE VEHICLE HAS CHANGED.PRICE OF THE VEHICLE HAS CHANGED.PRICE OF THE VEHICLE HAS CHANGED.PRICE OF THE VEHICLE HAS CHANGED.
-
MICROSOFT EXCEL OUTPUT
0
1 !"2 '
4'"(&( "
-!5 +*
-!6 '+ ******
-!0'" '+! %!!
-"
""(6 "+'+%+
0&"(8"- +!
;"!*%"!"
+"
4"+9 ;'+*+"""
!!9 '+*+"""
!9 * .;"
=: !"
POPULATION VARIANCE
.0001
23452.00
HHHH0 0 0 0 :=
HHHH1111 :
).105-
Reject HHHH0 0 0 0 if is very LARGE or very SMALL
6
-
EXAMPLE
& / 8 #
#
#
'% ' + ' " '* %
'! '
#/
'6+6
X = PERCENTAGE FAT CONTENT IN MUTTON
23452.00
HHHH0 0 0 0 :=20
HHHH1 1 1 1 : 20202020
= 25.82
.00010
X = PERCENTAGE FAT CONTENT IN MUTTON
!"#
$ %&'("
3.33 < 3.33 < 3.33 < 3.33 < < 16.9< 16.9< 16.9< 16.9
we cannot reject Hwe cannot reject Hwe cannot reject Hwe cannot reject H0 0 0 0 with 90% confidence with 90% confidence with 90% confidence with 90% confidence
(at 10% level of significance)(at 10% level of significance)(at 10% level of significance)(at 10% level of significance)
777
-
POPULATION PROPORTION
.0001
23452.00
HHHH0 0 0 0 : HHHH1111 ::::
).105-
Reject HHHH0 0 0 0 if is very LARGE or very SMALL
DEFECTIVE CUPS EXAMPLE
4
" 2
#
#+
#
##
7
-
0&8=;''"
If Z < 1.64 If Z < 1.64 If Z < 1.64 If Z < 1.64
we cannot reject Hwe cannot reject Hwe cannot reject Hwe cannot reject H0 0 0 0 with 95% confidence with 95% confidence with 95% confidence with 95% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
PACKAGE DESIGNER EXAMPLE
#
-
----1.96 < Z < 1.961.96 < Z < 1.961.96 < Z < 1.961.96 < Z < 1.96
we cannot reject Hwe cannot reject Hwe cannot reject Hwe cannot reject H0 0 0 0 with 99% confidence with 99% confidence with 99% confidence with 99% confidence
(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)(at 5% level of significance)
----1.44 1.44 1.44 1.44
CANNOT SAY AVERAGE SPENDING HAS CANNOT SAY AVERAGE SPENDING HAS CANNOT SAY AVERAGE SPENDING HAS CANNOT SAY AVERAGE SPENDING HAS
CHANGED WITH 95% CONFIDENCE.CHANGED WITH 95% CONFIDENCE.CHANGED WITH 95% CONFIDENCE.CHANGED WITH 95% CONFIDENCE.
top related