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TESTING OF HYPOTHESIS
What is hypothesis?
Hypothesis simply mean assumption or sum supposition to be
proved or disproved .
Characteristics Of Hypothesis
Hypothesis should be clear and precise.
Hypothesis should be capable of being tested
Hypothesis should state relationship between variables if it
happens to be relational Hypothesis.
Hypothesis should be limited in scope and must be specific
Hypothesis should be in most simple terms
Hypothesis should be consistent with most known facts.
• Statisitcs and :A statistic is a characteristic of a
sample,whereas
• parameter : parameter is a characteristic of a population
Basic concepts concerning testing of
hypothesis?
Null hypothesis- an initial belief of statement about the
population parameter is called null hypothesis.Null Hypothesis
is generally symbolised as Ho
Alternative hypothesis- the hypothesis is complimentary to
the null hypothesis is called alternative hypothesis.
Alternative hypothesis is usually one which one wishes to prove
and the null hypothesis is the one which one wishes to
disprove
example
Suppose we want to test the hypothesis that the population mean
(u)is equal to the hypothesised mean (uH0)=100
Null Hypothesis is that the population mean is equal to the
hypothesized mean 100
H0 u=uH0=100
Ha u is not equal uH0
Ha:u>uHa
Ha:u<uHa
Level of significance
• It means the researcher is wiling to take risk of rejecting
the null hypothesis when it happens to true
Type 1 and type 2 error
Type 1- when null hypothesis is true we may rejected this is
called type 1 error this is denoted by Alfa is also called
producer risk.
Type 2- when null hypothesis is false we may accepted this
called type 2 error this is denoted by beta is also called
consumer risk.
Procedure of hypothesis testing
• Making a formal statement- the step consist is making a
formal statement of null hypothesis and also of the alternative
hypothesis
• Selecting a significance level- the hypothesis are tested
on a pre determined level of a significance and as such the
same should be specified generally in practice either 5% level
or 1% level is adopted for the purposes.
• Deciding the distribution- after deciding the level of
significance, the next step in hypothesis testing is to determine
the appropriate sampling distribution. The choice generally
remains between normal distribution and t- distribution.
• Selecting a random sample and computing an
appropriate value- another step is to select a random
sample (s) and compute an appropriate value from the sample
data concerning the test statistic utilizing the relevant
distribution. In another 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 expectation. If the null hypothesis were In fact
true.
• Comparing the probability- in this step we compare the
probability thus calculated with the specified value for Alfa the
significance level if our calculated value is less or equal than
our value of significance level null hypothesis is accepted and
if it is greater then our null hypothesis is rejected.
• Calculation of the probability- one has then to calculate
the probability that the sample result would diverge as widely
as it has from expectation. If the null hypothesis were In fact
true.
• Comparing the probability- in this step we compare the
probability thus calculated with the specified value for Alfa the
significance level if our calculated value is less or equal than
our value of significance level null hypothesis is accepted and
if it is greater then our null hypothesis is rejected.
TESTS OF HYPOTHESES
a) Parametric tests or standard tests
b) Non parametric tests
PARAMETRIC TESTS
Parametric tests usually assume certain properties of the
population from which we draw samples. In parametric test we
have to make assumptions about the population parameters
like mean, variance.
Important parametric tests
1.
2.
3.
4.
Z-test
t-test
x square test
F-test
Hypothesis testing of mean
In Hypothesis testing of mean, mean of the population can be
tested from given formula-
Hypothesis testing for differences
between means
In many decision-situations, we may be interested in knowing
whether the parameters of two populations are alike or
different.
For instance, we may be interested in testing whether female
workers earn less than male workers for the same job.
Hypothesis testing of
proportions
In hypothesis testing of proportions, proportions can be tested by
using probability.
Hypothesis testing for difference
between proportions
if two samples are drawn from different populations, one may be
interested in knowing whether the difference between the
proportion of successes is significant or not.