hypothesis testing-1 (1)

HYPOTHESIS

TESTING

INSURANCE CLAIM EXAMPLE

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EMPLOYEE ABSENTEEISM

EXAMPLE

$ # %

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#

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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)


.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




.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



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



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


) )

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



----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



*

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 :


!"#

$ %&'("#

*

Z > Z > Z > Z > ----1.791.791.791.79



)

----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 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"-

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4"+

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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

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) 7

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X = POLLUTION COUNT FOR THE CITY

23452.00

HHHH0 0 0 0 : 150 HHHH1111 : >>>> 150

N = 20 =150.7 S = 5.25

.00010


!"#

/

$ %&'("#

.

./

Z < 1.729Z < 1.729Z < 1.729Z < 1.729



)

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



---- 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



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



PACKAGE DESIGNER EXAMPLE

#

----1.96 < Z < 1.961.96 < Z < 1.961.96 < Z < 1.961.96 < Z < 1.96



----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.

hypothesis testing-1 (1)

Documents

p z p z p z p z

large p z

small p p p p

level of significanceat

level of significance

average spending

null hypothesis

alternative hypothesis