Download Null and Alternative Hypothesis

Unit 3
Tentative solutions proposed by the researcher
Intelligent and logical guesses about possible
differences, relationships, causes and solutions
 These may or may not be real solutions to the
problem
 Whether they are or not is to be tested by the
researcher
 A predictive statement , capable of being tested
by scientific methods that relates an
independent variable to dependent variable
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A tentative generalization, the validity of
which remains to be tested. In most
elementary stage hypothesis may be any
guess, hunch , imaginative idea which
becomes the basis for action or investigation
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Clarity
Empirically testable
Specific
Simple to understand
Consistency
Time bound
Consider all aspects of a problem
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Provides definite focus
Spells out the difference between precision
and haphazardness
Suggests the type of research
Suggests the type of analysis
Helps to develop theory
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Null and Alternative hypothesis
Null Hypothesis
 If we are to compare method A with method B about
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its superiority and if we proceed on the assumption
that both methods are equally good, then this
assumption is termed as Null hypothesis
 Symbolized as Ho
Alternative Hypothesis
 We may think that method A is superior and method
B is inferior, then this assumption is Alternative
hypothesis
 Symbolized as Ha
Suppose we assume that the mean attendance of a class is
70.
Null hypothesis
 H0 :µ= µ H0 =70 (Null hypothesis is that the mean
attendance of a class is 70)
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Alternative Hypothesis
 Ha : µ≠ µ H0 (The alternative hypothesis is that mean
attendance of class is not equal to 70. It may be more or
less than 70)
 Ha : µ> µ H0 (The alternative hypothesis is that mean
attendance of class is greater than 70)
 Ha : µ< µ H0 (The alternative hypothesis is that mean
attendance of class is less than 70)
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Alternative hypothesis is usually the one
which one wishes to prove and null
hypothesis is the one which one wishes to
disprove
Null hypothesis represents the hypothesis we
are trying to reject and alternative hypothesis
represents all other possibilities
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Usually taken as 5% or sometimes 1%
5% level of significance means
 Ho will be rejected when the result has less than
5%(.05) probability of occurring if Ho is true
 Researcher is willing to take as much as 5% risk of
rejecting Ho when it happens to be true
 Level of significance is the maximum level of the
probability of rejecting null hypothesis when it is
true.
 Usually determined in advance
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Given a hypothesis Ho and an alternative
hypothesis Ha, we make a rule called decision
rule according to which we accept Ho or reject Ho
If Ho is that a student is punctual( he/she is never
late for the class) and Ha is that the student is
not punctual ( he/she is usually late for the class),
then we must decide the number of times to be
tested and the criterion for accepting or
rejecting H0.
We might test in 20 classes and plan our decision
saying that if the student is on time up to 18
times we accept Ho else reject Ho.
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Type 1 Error
 Rejecting Ho when Ho is true
 Denoted by α (alpha)
 Also called level of significance of test
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Type 2 Error
 Accepting Ho when Ho is false
 Denoted by β
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A two tailed test rejects null hypothesis if
sample mean is significantly higher or lower
than the hypothesized mean
It is appropriate when null hypothesis is some
specified value and alternative hypothesis is
not equal to the null hypothesis value.
Symbolically, two tailed test is appropriate
when
H0 :µ= µ H0 and Ha : µ≠ µ H0
A one tailed test is appropriate if we are to test
whether sample mean is either significantly higher or
lower than the hypothesized mean
 It is appropriate when null hypothesis is some
specified value and alternative hypothesis is either
greater than or less than the null hypothesis value
 Symbolically, two tailed test is appropriate when
H0 :µ= µ H0 and Ha : µ> µ H0 (Right tailed test)
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OR
H0 :µ= µ H0 and Ha : µ< µ H0 (Left tailed test)
Left tailed test
Right tailed test
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Steps undertaken to make a choice between
accepting or rejecting null hypothesis
Making a formal statement
 Both null and alternative hypothesis clearly stated
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Selecting a significance level
 Generally 5% or 1%
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Deciding the distribution to use
 T-distribution or normal distribution
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Compute statistics
Calculate probability that sample result would
diverge as widely as it has from expectations
Compare probability with specified level of
significance
 If calculated probability < α in one tailed or α/2 in two
tailed test, reject Ho
 If calculated probability > α in one tailed or α/2 in two
tailed test, accept Ho
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Parametric tests
 Used with normal distribution
 Z-test, t-test, chi-square test, f-test
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Non parametric tests
 Distribution free
 Sign test , Fisher-Irwin test, Signed rank test, rank sum
tests etc.
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Correlation Analysis
 Finding out if there is a relationship between two or more
variables
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Regression Analysis
 To establish cause and effect relationship between two
variables