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.


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