testing of hypothesiss.ppt

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					       TESTING OF HYPOTHESIS

1):-Construction of hypotheses
2):- Level of significance
3):- Test statistic
4):-Decision rule
5):-Conclusion
EXAMPLE:- It is claimed that an automobile is driven on the
average more than 12,000 miles per year. To test this claim a
random sample of 100 automobiles owners are asked to keep
a record of the miles they travel. Would you agree with the
claim if the random sample showed an average of 12500
miles and a standard deviation of 2400 miles?
                      Construction of hypotheses
   POPULATION            Ho :   12000
    > 12000             H1:  > 12000
      12000        Level of significance
                                        = 5%
                Test Statistic

                                      X        12500 12000
                                 Z=          =                 2.083
                                       s2           (2400 ) 2

  SAMPLE                               n              100
  n=100                Decision Rule:- Reject Ho if Zcal  Z
  X=12500
  S=2400                  Result:-As Zcal > Z.05 =1.645, So reject Ho and conclude
                          that the claim is true.
EXAMPLE:- It has been found from experience that the mean
breaking strength of a particular brand of thread is 9.63N with
a standard deviation of 1.40N. Recently a sample of 36 pieces
of thread showed a mean breaking strength of 8.93N. Can we
conclude that the thread has become inferior?

                     Construction of hypotheses
   POPULATION
                            Ho :   9.63
      =1.40
                            H1:  < 9.63
    < 9.63
      9.63        Level of significance
                                       = 5%
                Test Statistic

                                      X          8.93  9.63
                                 Z=                              3
                                          2
                                                     (1.40) 2
                                        n               36
  SAMPLE
  n=36                Decision Rule:- Reject Ho if Zcal  - Z
  X=8.93
                         Result:-As Zcal < - Z.05= -1.645 Reject Ho and hence we
                         conclude that threat has become inferior.
EXAMPLE:- Workers at a production facility are required to assemble a certain part in 2.3
minutes in order to meet production criteria. The assembly rate per part is assumed to be
normally distributed. Six workers are selected at random and time in assembling is recorded.
The assembly times (in minutes) for the six workers are as follows. The manager wants to
determine that the mean assembling time is according to production criteria.
 Worker         1            2              3             4               5      6      TOTAL
 Time           2            2.4            1.7           1.9             2.8    1.8    12.6
       2
 (X-X)          0.01         0.09           0.16          0.04            0.49   0.09   0.88
  X 
       X  12.6  2.1       S2 
                                   ( X  X )  0.88  0.176
                                             2

       n      6                           n 1          5
                         Construction of hypotheses
     POPULATION                          Ho:   2.3
                                         H1:  > 2.3
      2.3
      >2.3              Level of significance
                                            = 5%
                  Test Statistic

                                        X        2.1  2.3
                                   t=          =                1.166
                                          2
                                         S          0.176
   SAMPLE                                 n           6

   n=6
   X=2.1                  Decision Rule:-Reject Ho if tcal  t(n-1)
   S2=0.176
                             Result:-As tcal < t.05 (5),= 2.015 So don’t reject Ho and
                             conclude that the assembling time is according to production
                             criteria.
Test of hypothesis for population mean
Ho       H1          Population variance        Test Statistic   Decision rule
                      Sample size                                Reject Ho if
  µo    > µo       Pop. Variance known                       Zcal > Z
                                                     X 
                                                Z
                                                       2
                                                        n
  µo    < µo         Pop.Variance unknown                    Zcal < -Z
                                                    X 
                         Large sample           Z
                                                       S2
                                                       n
 = µo        µo      Pop.Variance unknown                    Zcal > Z/2
                                                    X 
                         Large sample           Z                      OR
                                                       S2          Zcal < -Z/2
                                                       n
 = µo        µo      Pop.Variance unknown                         > t/2(n-1)
                                                     X 
                                                                 tcal
                        Small sample           t                        OR
                                                       S2        tcal < -t/2(n-1)
                                                       n

				
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