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Testofhypothesis
Introduction
Hypothesis is usually considered as the principal
 instrument in research.
Its main function is to suggest new experiments
 and observations.
In fact, many experiments are carried out with
 the deliberate object of testing hypotheses.
Decision-makers often face situations where in
 they are interested in testing hypotheses on the
 basis of available information and then take
 decisions on the basis of such testing.
• Ordinarily, when one talks about hypothesis, one simply
  means a mere assumption or some supposition to be proved
  or disproved.
• But for a researcher hypothesis is a formal question that he
  intends to resolve.
• Thus a hypothesis may be defined as a proposition or a set of
  proposition set forth as an explanation for the occurrence of
  some specified group of phenomena either asserted merely as
  a provisional conjecture to guide some investigation or
  accepted as highly probable in the light of established facts.
• Quite often a research hypothesis is a predictive statement,
  capable of being tested by scientific methods, that relates an
  independent variable to some dependent variable.


                              What Is A Hypothesis?
WHAT IS A HYPOTHESIS...
Example
The mileage of automobile A is as
 good as automobile b
The customer loyalty of brand A
 is better than brand B.
These hypotheses are capable of
 objectively verified and tested
STEPS IN HYPOTHESIS TESTING PROCEDURE
                  EVALUATE DATA

               REVIEW ASSUMPTIONS

                STATE HYPOTHESIS

              SELECT TEST STATISTICS

   DETERMINE DISTRIBUTION OF TEST STATISTICS

                  State decision rule

              CALCULATE TEST STATISTICS

   Do not         MAKE STATISTICAL         Reject
  Reject H0          DECISION                  H0

Conclude H0                               Conclude H1
May be true                                 Is true
Characteristics of a hypothesis
 Conceptual Clarity -Hypothesis should be clear
                      -
  and precise.
 Testability -Hypothesis should be capable of
              -
  being tested.
 Consistency - It should be consistent with the
  objectives of research.
 Expectancy -Hypothesis should be able to state
                -
  relationship between variables, if it happens to
  be a relational hypothesis.
 Specificity -Hypothesis should be limited in
              -
  scope and must be specific. Narrower
  hypothesis are easily testable.
 Simplicity -Hypothesis should be stated as far
             -
  as possible in most simple terms so that the
  same is easily understandable by all
  concerned.
 Theoretical Relevance -Hypothesis should be
                           -
  consistent with most known facts i.e., it must
  be consistent with a substantial body of
  established facts.
Objectivity - It should not include value
 judgments, relative terms or any moral
 preaching.
Availability of Techniques – Statistical
 methods should be available for testing the
 proposed hypothesis.
Hypothesis should be amenable to testing
 within a reasonable time
Hypothesis must explain the facts that give
 rise to the need for explanation
Testofhypothesis
Parametric and Standard Test
 BASIC CONCEPTS CONCERNING TESTING OF
  HYPOTHESES
  Null hypothesis and alternative hypothesis
  The level of significance
  Decision rule or test of hypothesis
  Type I and Type II Errors
  Two-tailed and One-tailed tests
Basic concepts concerning testing of
             hypothesis
Null Hypothesis and alternative hypothesis
• In statistical analysis if we want to compare
  method A with method B and if we proceed with
  the assumption that both methods are equally
  good then this assumption is termed as null
  hypothesis.
Basic concepts concerning testing of
               hypothesis

• As against this we may feel that method A is
  better than method B then we call it as
  alternative hypothesis


• Null Hypothesis is generally is termed as H0

• Alternative hypothesis symbolized as Ha
Basic concepts concerning testing of
                hypothesis
• Suppose we want to test the hypothesis that the
  population mean (µ) is equivalent to
  hypothesised mean then (µH0 )= 100
• Then null hypothesis would be population
  mean is equal to hypothesised mean


•                 Ho: µ= µHo = 100
Three Possible alternative hypotheses
Alternative hypothesis   To be read as follows

Ha : µ ≠µH0              The alternative hypothesis is that the
                         population mean is not equal to 100
                         i.e., it may be more or less than 100

Ha : µ > µH              The alternative hypothesis is that the
              0
                         population mean is greater than 100

Ha : µ < µH0             The alternative hypothesis is that the
                         population mean is less than 100
Possible Rejection and Nonrejection
              Regions
                        Rejection region
                        for hypothesis
                        which involve
                        the
                        standard normal
                        distribution and
                        the ≠ symbol
                        (two –tailed test)
Possible Rejection and Nonrejection
             Regions
                         Rejection region
                         for hypothesis
                         which involve
                         the
                         standard normal
                         distribution and
                         the > symbol
                         (right –tailed
                         test)
Possible Rejection and Nonrejection
              Regions

                         Rejection region
                         for hypothesis
                         which involve
                         the
                         standard normal
                         distribution and
                         the < symbol
                         (left –tailed test)
In the choice of null hypothesis, the following
considerations are usually kept in view:


 • Alternative hypothesis is usually the one which one
   wishes to prove and the null hypothesis is the one
   which one wishes to disprove.
 • Thus, a null hypothesis represents the hypothesis we
   are trying to reject, and alternative hypothesis
   represents all other possibilities
In the choice of null hypothesis, the following
 considerations are usually kept in view:

• If the rejection of a certain hypothesis when it is actually
  true involves great risk, it is taken as null hypothesis
  because then the probability of rejecting it when it is
  true is α (the level of significance) which is chosen very
  small.
• Null hypothesis should always be specific hypothesis
  i.e., it should not state about or approximately a certain
  value.
The level of significance
• This is a very important concept in the context of
  hypothesis testing.
• It is always some percentage (usually 5%) which should
  be chosen wit great care, thought an reason. In case we
  take the significance level at 5 per cent, then this implies
  that H0 will be rejected
• If a hypothesis is of the type µ =µH0, then we call such
  a hypothesis as simple (or specific) hypothesis but if it
  is of the type µ ≠ µH0 or µ> µH0 or µ<µH0 then we call it
  a composite (or nonspecific) hypothesis.
Decision rule or test of hypothesis
• Given a hypothesis H0 and an alternative hypothesis Ha, we
  make a rule which is known as decision rule according to
  which we accept H0 (i.e., reject Ha) or reject H0 (i.e., accept
  Ha).
• For instance, if (H0 is that a certain lot is good (there are
  very few defective items in it) against Ha) that the lot is not
  good (there are too many defective items in it), then we
  must decide the number of items to be tested and the
  criterion for accepting or rejecting the hypothesis.
• We might test 10 items in the lot and plan our decision
  saying that if there are none or only1 defective item among
  the 10, we will accept H0 otherwise we will reject H0 (or
  accept Ha). This sort of basis is known as decision rule.
Type I and Type II errors
We may reject H0when H0is true and we may accept H0
when in fact H0 is not true. The former is known as
 Type I error and the latter as Type II error.
• Type I Error
   – Rejecting a true null hypothesis
   – Type I error means rejection of hypothesis which should
     have been accepted
   – The probability of committing a Type I error is called α,
     the level of significance.
• Type II Error
   – Failing to reject a false null hypothesis
   – Type II error means accepting the hypothesis which
     should have been rejected.
   – The probability of committing a Type II error is called β.
Type I and Type II Errors

                                    State of World

      Decision         Ho true                 H1 true (Ho false)

  Cannot reject        Correct                 Type II error
  (“accept”) Ho        decision

  Reject Ho            Type I error            Correct decision

              Need to control both types of error:
                  α = P(rejecting Ho|Ho)
                  β = P(not rejecting Ho|H1)
Type I and Type II Errors
• Definition: Type I and Type II errors
A Type I error is the error of rejecting H0 when it is true. A Type II
error is the error of accepting H0 when it is false (that is when H1 is
true).
• Notation:     Probability of Type I error: a = P[X ∈ R|H0]
               Probability of Type II error: b = P[X ∈ RC|H1]


• Definition: Power of the test
The probability of rejecting H0 based on a test procedure is called the
power of the test. It is a function of the value of the parameters tested,
θ:
        π = π(θ) = P[X ∈ R].
       Note: when θ ∈ H1         => π(θ) = 1- b(θ).
Type I and Type II Errors
• We want π(θ) to be near 0 for θ ∈ H0, and π(θ) to be near 1 for θ
∈ H1.


• Definition: Level of significance
When θ ∈ H0 α, π(θ) gives you the probability of Type I error. This
probability depends on θ. The maximum value of this when θ ∈ H0
is called level of significance (significance level) of a test, denoted
by α. Thus,
                 α = supθ ∈ H0 P[X ∈ R|H0] = supθ ∈ H0 π(θ)

Define a level α test to be a test with supθ ∈ H0 π(θ) ≤ α.
Sometimes, α. is called the size of a test.
Type I and Type II Errors
                                      0.9



                                      0.8



                                      0.7



                                      0.6



                                      0.5



                                      0.4



                                      0.3



                                      0.2



                                      0.1



                                       0
    -1.50      -1.00    -0.50           0.00        0.50       1.00      1.50

                                       H0      H1

    β = Type II error
                                                           α = Type I error

                                π = Power of test
TWO TAILED AND ONE TAILED TEST

• A two tailed test reject the null hypothesis if, say the
  sample mean is significantly higher or lower than the
  hypothesised value of mean population.
• Symbolically, the two tailed test is appropriate when we
  have H₀:μ=μH₀ and Ha: μ≠ μH₀ which may mean
  μ>μH₀ or μ<μH₀.
• Thus, in a two tailed test, there are two rejection regions.
A one tailed test is used when we have to test whether population
mean is either lower than or higher than some hypothesised
value.
In this if the rejection region on the left it is called left tailed
test .It is represented as-

H₀: μ= μH₀ and Ha: μ< μH₀

 If the rejection is on the right side it is called right tailed test.
It is denoted by

H₀: μ= μH₀ and Ha: μ> μH₀
Testofhypothesis
Testofhypothesis
Testofhypothesis
One-tail vs. Two-tail Test
One-Tailed Test versus Two-Tailed Test
PROCEDURE FOR HYPOTHESIS TESTING
• Procedure for hypothesis testing refers to all those steps
  that we undertake for making a choice between the two
  actions i.e., rejection and acceptance of a null hypothesis.
  The various steps involved in hypothesis testing are stated
  below:
 Making a formal statement
 Selecting a significance level
 Deciding the distribution to use
 Selecting a random sample and computing an appropriate value
 Calculation of the probability
 Comparing the probability
Making a formal statement
• The step consists in making a formal statement of the null
  hypothesis (H0) and also of the alternative hypothesis (Ha).
  This means that hypotheses should be clearly stated,
  considering the nature of the research problem.
• For instance, Mr. Mohan of the Civil Engineering
  Department wants to test the load bearing capacity of an
  old bridge which must be more than 10 tons, in that case
  he can state his hypotheses as under:

   – Null hypothesis H0 : µ = 10 tons
   – Alternative Hypothesis Ha: µ > 10 tons
Making a formal statement…
• Take another example. The average score in an
  aptitude test administered at the national level is 80.
• To evaluate a state’s education system, the average
  score of 100 of the state’s students selected on
  random basis was 75. The state wants to know if there
  is a significant difference between the local scores
  and the national scores. In such a situation the
  hypotheses may be stated as under:
              • Null hypothesis H0: µ = 80
          • Alternative HypothesisHa: µ ≠ 80
Making a formal statement…
• The formulation of hypotheses is an important step
  which must be accomplished with due care in
  accordance with the object and nature of the
  problem under consideration.
• It also indicates whether we should use a one-tailed
  test or a two-tailed test. If Ha is of the type greater
  than (or of the type lesser than), we use a one-tailed
  test, but when Ha is of the type “whether greater or
  smaller” then we use a two-tailed test.
Selecting a significance level
• The hypotheses are tested on a pre-determined level of
  significance and as such the same should be specified.
  Generally, in practice, either 5% level or 1% level is
  adopted for the purpose. The factors that affect the level
  of significance are:
    the magnitude of the difference between sample means;
    the size of the samples;
    the variability of measurements within samples;
    whether the hypothesis is directional or non-directional (A
     directional hypothesis is one which predicts the direction of the
     difference between, say, means).
• The level of significance must be adequate in the context
  of the purpose and nature of enquiry.
Deciding the distribution to use
• Hypothesis testing is to determine the appropriate
  sampling distribution.
• The choice generally remains between normal
  distribution and the t-distribution.
• The rules for selecting the correct distribution are
  similar to those which we have stated earlier in the
  context of estimation.
Selecting a random sample and computing
           an appropriate value
• Select a random sample(s) and
  compute an appropriate value
  from the sample data concerning
  the test statistic utilizing the
  relevant distribution.

• In other words, draw a sample
  to furnish empirical data.
Calculation of the probability


• One has then to calculate the probability that the
  sample result would diverge as widely as it has from
  expectations, if the null hypothesis were in fact true.
Comparing the probability
• Comparing the probability thus calculated with the
  specified value for α the significance level.
• If the calculated probability is equal to or smaller than
  the α value in case of one-tailed test (and α/2 in case of
  two-tailed test), then reject the null hypothesis (i.e., accept
  the alternative hypothesis), but if the calculated
  probability is greater, then accept the null hypothesis.
• In case we reject Ho we run a risk of (at most the level
  of significance),committing an error of Type I, but if we
  accept H0, then we run some risk (the size of which
  cannot be specified as long as the H0 happens to be vague
  rather than specific) of committing an error of Type II.
•  
Testofhypothesis
conclusion
• From this I conclude that “ an effective
  research can’t be fulfill the objectives
  without Hypothesis”
• So a researcher should have a thorough
  knowledge in this field of fixing and
  testing of hypothesis.
Testofhypothesis

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Testofhypothesis

  • 2. Introduction Hypothesis is usually considered as the principal instrument in research. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate object of testing hypotheses. Decision-makers often face situations where in they are interested in testing hypotheses on the basis of available information and then take decisions on the basis of such testing.
  • 3. • Ordinarily, when one talks about hypothesis, one simply means a mere assumption or some supposition to be proved or disproved. • But for a researcher hypothesis is a formal question that he intends to resolve. • Thus a hypothesis may be defined as a proposition or a set of proposition set forth as an explanation for the occurrence of some specified group of phenomena either asserted merely as a provisional conjecture to guide some investigation or accepted as highly probable in the light of established facts. • Quite often a research hypothesis is a predictive statement, capable of being tested by scientific methods, that relates an independent variable to some dependent variable. What Is A Hypothesis?
  • 4. WHAT IS A HYPOTHESIS... Example The mileage of automobile A is as good as automobile b The customer loyalty of brand A is better than brand B. These hypotheses are capable of objectively verified and tested
  • 5. STEPS IN HYPOTHESIS TESTING PROCEDURE EVALUATE DATA REVIEW ASSUMPTIONS STATE HYPOTHESIS SELECT TEST STATISTICS DETERMINE DISTRIBUTION OF TEST STATISTICS State decision rule CALCULATE TEST STATISTICS Do not MAKE STATISTICAL Reject Reject H0 DECISION H0 Conclude H0 Conclude H1 May be true Is true
  • 6. Characteristics of a hypothesis  Conceptual Clarity -Hypothesis should be clear - and precise.  Testability -Hypothesis should be capable of - being tested.  Consistency - It should be consistent with the objectives of research.  Expectancy -Hypothesis should be able to state - relationship between variables, if it happens to be a relational hypothesis.
  • 7.  Specificity -Hypothesis should be limited in - scope and must be specific. Narrower hypothesis are easily testable.  Simplicity -Hypothesis should be stated as far - as possible in most simple terms so that the same is easily understandable by all concerned.  Theoretical Relevance -Hypothesis should be - consistent with most known facts i.e., it must be consistent with a substantial body of established facts.
  • 8. Objectivity - It should not include value judgments, relative terms or any moral preaching. Availability of Techniques – Statistical methods should be available for testing the proposed hypothesis. Hypothesis should be amenable to testing within a reasonable time Hypothesis must explain the facts that give rise to the need for explanation
  • 10. Parametric and Standard Test  BASIC CONCEPTS CONCERNING TESTING OF HYPOTHESES Null hypothesis and alternative hypothesis The level of significance Decision rule or test of hypothesis Type I and Type II Errors Two-tailed and One-tailed tests
  • 11. Basic concepts concerning testing of hypothesis Null Hypothesis and alternative hypothesis • In statistical analysis if we want to compare method A with method B and if we proceed with the assumption that both methods are equally good then this assumption is termed as null hypothesis.
  • 12. Basic concepts concerning testing of hypothesis • As against this we may feel that method A is better than method B then we call it as alternative hypothesis • Null Hypothesis is generally is termed as H0 • Alternative hypothesis symbolized as Ha
  • 13. Basic concepts concerning testing of hypothesis • Suppose we want to test the hypothesis that the population mean (µ) is equivalent to hypothesised mean then (µH0 )= 100 • Then null hypothesis would be population mean is equal to hypothesised mean • Ho: µ= µHo = 100
  • 14. Three Possible alternative hypotheses Alternative hypothesis To be read as follows Ha : µ ≠µH0 The alternative hypothesis is that the population mean is not equal to 100 i.e., it may be more or less than 100 Ha : µ > µH The alternative hypothesis is that the 0 population mean is greater than 100 Ha : µ < µH0 The alternative hypothesis is that the population mean is less than 100
  • 15. Possible Rejection and Nonrejection Regions Rejection region for hypothesis which involve the standard normal distribution and the ≠ symbol (two –tailed test)
  • 16. Possible Rejection and Nonrejection Regions Rejection region for hypothesis which involve the standard normal distribution and the > symbol (right –tailed test)
  • 17. Possible Rejection and Nonrejection Regions Rejection region for hypothesis which involve the standard normal distribution and the < symbol (left –tailed test)
  • 18. In the choice of null hypothesis, the following considerations are usually kept in view: • Alternative hypothesis is usually the one which one wishes to prove and the null hypothesis is the one which one wishes to disprove. • Thus, a null hypothesis represents the hypothesis we are trying to reject, and alternative hypothesis represents all other possibilities
  • 19. In the choice of null hypothesis, the following considerations are usually kept in view: • If the rejection of a certain hypothesis when it is actually true involves great risk, it is taken as null hypothesis because then the probability of rejecting it when it is true is α (the level of significance) which is chosen very small. • Null hypothesis should always be specific hypothesis i.e., it should not state about or approximately a certain value.
  • 20. The level of significance • This is a very important concept in the context of hypothesis testing. • It is always some percentage (usually 5%) which should be chosen wit great care, thought an reason. In case we take the significance level at 5 per cent, then this implies that H0 will be rejected • If a hypothesis is of the type µ =µH0, then we call such a hypothesis as simple (or specific) hypothesis but if it is of the type µ ≠ µH0 or µ> µH0 or µ<µH0 then we call it a composite (or nonspecific) hypothesis.
  • 21. Decision rule or test of hypothesis • Given a hypothesis H0 and an alternative hypothesis Ha, we make a rule which is known as decision rule according to which we accept H0 (i.e., reject Ha) or reject H0 (i.e., accept Ha). • For instance, if (H0 is that a certain lot is good (there are very few defective items in it) against Ha) that the lot is not good (there are too many defective items in it), then we must decide the number of items to be tested and the criterion for accepting or rejecting the hypothesis. • We might test 10 items in the lot and plan our decision saying that if there are none or only1 defective item among the 10, we will accept H0 otherwise we will reject H0 (or accept Ha). This sort of basis is known as decision rule.
  • 22. Type I and Type II errors We may reject H0when H0is true and we may accept H0 when in fact H0 is not true. The former is known as Type I error and the latter as Type II error. • Type I Error – Rejecting a true null hypothesis – Type I error means rejection of hypothesis which should have been accepted – The probability of committing a Type I error is called α, the level of significance. • Type II Error – Failing to reject a false null hypothesis – Type II error means accepting the hypothesis which should have been rejected. – The probability of committing a Type II error is called β.
  • 23. Type I and Type II Errors State of World Decision Ho true H1 true (Ho false) Cannot reject Correct Type II error (“accept”) Ho decision Reject Ho Type I error Correct decision Need to control both types of error: α = P(rejecting Ho|Ho) β = P(not rejecting Ho|H1)
  • 24. Type I and Type II Errors • Definition: Type I and Type II errors A Type I error is the error of rejecting H0 when it is true. A Type II error is the error of accepting H0 when it is false (that is when H1 is true). • Notation: Probability of Type I error: a = P[X ∈ R|H0] Probability of Type II error: b = P[X ∈ RC|H1] • Definition: Power of the test The probability of rejecting H0 based on a test procedure is called the power of the test. It is a function of the value of the parameters tested, θ: π = π(θ) = P[X ∈ R]. Note: when θ ∈ H1 => π(θ) = 1- b(θ).
  • 25. Type I and Type II Errors • We want π(θ) to be near 0 for θ ∈ H0, and π(θ) to be near 1 for θ ∈ H1. • Definition: Level of significance When θ ∈ H0 α, π(θ) gives you the probability of Type I error. This probability depends on θ. The maximum value of this when θ ∈ H0 is called level of significance (significance level) of a test, denoted by α. Thus, α = supθ ∈ H0 P[X ∈ R|H0] = supθ ∈ H0 π(θ) Define a level α test to be a test with supθ ∈ H0 π(θ) ≤ α. Sometimes, α. is called the size of a test.
  • 26. Type I and Type II Errors 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 H0 H1 β = Type II error α = Type I error π = Power of test
  • 27. TWO TAILED AND ONE TAILED TEST • A two tailed test reject the null hypothesis if, say the sample mean is significantly higher or lower than the hypothesised value of mean population. • Symbolically, the two tailed test is appropriate when we have H₀:μ=μH₀ and Ha: μ≠ μH₀ which may mean μ>μH₀ or μ<μH₀. • Thus, in a two tailed test, there are two rejection regions.
  • 28. A one tailed test is used when we have to test whether population mean is either lower than or higher than some hypothesised value. In this if the rejection region on the left it is called left tailed test .It is represented as- H₀: μ= μH₀ and Ha: μ< μH₀ If the rejection is on the right side it is called right tailed test. It is denoted by H₀: μ= μH₀ and Ha: μ> μH₀
  • 33. One-Tailed Test versus Two-Tailed Test
  • 34. PROCEDURE FOR HYPOTHESIS TESTING • Procedure for hypothesis testing refers to all those steps that we undertake for making a choice between the two actions i.e., rejection and acceptance of a null hypothesis. The various steps involved in hypothesis testing are stated below:  Making a formal statement  Selecting a significance level  Deciding the distribution to use  Selecting a random sample and computing an appropriate value  Calculation of the probability  Comparing the probability
  • 35. Making a formal statement • The step consists in making a formal statement of the null hypothesis (H0) and also of the alternative hypothesis (Ha). This means that hypotheses should be clearly stated, considering the nature of the research problem. • For instance, Mr. Mohan of the Civil Engineering Department wants to test the load bearing capacity of an old bridge which must be more than 10 tons, in that case he can state his hypotheses as under: – Null hypothesis H0 : µ = 10 tons – Alternative Hypothesis Ha: µ > 10 tons
  • 36. Making a formal statement… • Take another example. The average score in an aptitude test administered at the national level is 80. • To evaluate a state’s education system, the average score of 100 of the state’s students selected on random basis was 75. The state wants to know if there is a significant difference between the local scores and the national scores. In such a situation the hypotheses may be stated as under: • Null hypothesis H0: µ = 80 • Alternative HypothesisHa: µ ≠ 80
  • 37. Making a formal statement… • The formulation of hypotheses is an important step which must be accomplished with due care in accordance with the object and nature of the problem under consideration. • It also indicates whether we should use a one-tailed test or a two-tailed test. If Ha is of the type greater than (or of the type lesser than), we use a one-tailed test, but when Ha is of the type “whether greater or smaller” then we use a two-tailed test.
  • 38. Selecting a significance level • The hypotheses are tested on a pre-determined level of significance and as such the same should be specified. Generally, in practice, either 5% level or 1% level is adopted for the purpose. The factors that affect the level of significance are:  the magnitude of the difference between sample means;  the size of the samples;  the variability of measurements within samples;  whether the hypothesis is directional or non-directional (A directional hypothesis is one which predicts the direction of the difference between, say, means). • The level of significance must be adequate in the context of the purpose and nature of enquiry.
  • 39. Deciding the distribution to use • Hypothesis testing is to determine the appropriate sampling distribution. • The choice generally remains between normal distribution and the t-distribution. • The rules for selecting the correct distribution are similar to those which we have stated earlier in the context of estimation.
  • 40. Selecting a random sample and computing an appropriate value • Select a random sample(s) and compute an appropriate value from the sample data concerning the test statistic utilizing the relevant distribution. • In other words, draw a sample to furnish empirical data.
  • 41. Calculation of the probability • One has then to calculate the probability that the sample result would diverge as widely as it has from expectations, if the null hypothesis were in fact true.
  • 42. Comparing the probability • Comparing the probability thus calculated with the specified value for α the significance level. • If the calculated probability is equal to or smaller than the α value in case of one-tailed test (and α/2 in case of two-tailed test), then reject the null hypothesis (i.e., accept the alternative hypothesis), but if the calculated probability is greater, then accept the null hypothesis. • In case we reject Ho we run a risk of (at most the level of significance),committing an error of Type I, but if we accept H0, then we run some risk (the size of which cannot be specified as long as the H0 happens to be vague rather than specific) of committing an error of Type II. •  
  • 44. conclusion • From this I conclude that “ an effective research can’t be fulfill the objectives without Hypothesis” • So a researcher should have a thorough knowledge in this field of fixing and testing of hypothesis.