testing of hypothesis

1. Testing Of Hypothesis
Shri Vaishnav Institute of Management, Indore
Department of Computer Science
MCA I Year I Semester
2022-23
MCA-102 : Statistical Mathematics
Unit-III
By
Dr. Bharti Agrawal
Assistant Professor

2. Introduction
• Inferential statistics is concerned with
(i) Estimating the true value of population
parameters using sample statistics (Estimation
Theory) and
(ii) Testing of hypothesis or Test of Significance

3. Hypothesis
 A statistical hypothesisis
 an assumption about any aspect of a population
 is simply a quantitative statement about population
 a claim (assertion, statement, belief or assumption) about an
unknown population parameter value
 It could be the parameters of a distribution like mean of
Normal distribution, describing the population, the
parameters of two or more populations, correlation or
association between two or more characteristics of a
population like age and height, etc.

4. Hypothesis: Example
1. A judge assumesthat
 A person charged with a crime is innocent
and subject this assumption (hypothesis) to a
verification by reviewing the evidence and hearing
testimony before reaching to a decision
2. A pharmaceutical company claims that
 The efficacy of a medicine against a disease that 95 % of all
persons suffering from the said disease get cured
3. An investment company claims that the average return
across all its investments is 20 percent

5. Hypothesis Testing
 To test such claims or assertions statistically, sample data are
collected and analyzed
 On the basis of sample findings the hypothesis of the
population parameter is either accepted or rejected.
 The process that enables a decision maker to test the validity
(or significance) of this claim by analysing the difference
between the value of sample statistic and the corresponding
hypothesized population parameter value, is called
hypothesis testing

6. Procedure for Hypothesis Testing
1. State the Null Hypothesis (H0) and Alternative
Hypothesis (H1)
2. Selectthe Suitable Test Statistic
3. State the Level of Significance, α
4. Establish Critical or Rejection Region
5. Formulate a Decision Rule to Accept or
Reject the Null Hypothesis

7. Null Hypothesis
 A definite statement about the populationparameter(s)
 Such a statistical hypothesis which is under test, is usually
a hypothesis of no difference and hence is called null
hypothesis
 A hypothesis which is the hypothesis of no difference is
null hypothesis
 The null hypothesis presumes that there is no difference
between sample statistic and the parameter value
 Example: H0: μ = μ0.

8. Alternative Hypothesis
 Any hypothesis which is complementary to the null
hypothesis is called an alternative hypothesis. It is
usually denoted by H1
 Acceptance or rejection of null hypothesis is meaningful
only when it is being tested against a rival hypothesis
which should rather be explicitly mentioned
 Example:
H1: μ ≠ μ0.
H1: μ > μ0.
H1: μ < μ0.

9. Selection of Test Statistic
 For choosing a particular test statistic following
three factors are considered:
 Whether the test involves one sample, two samples, or k
samples?
 Whether two or more samples used are independent or related?
 Is the measurement scale nominal, ordinal, interval, or ratio?
 Further, it is also important to know:
 Sample size
 The number of samples and their size

10. Level of Significance (α)
 The level of significance defines the likelihood of
rejecting a null hypothesis when it is true, i.e. it
is the risk a decision-maker takes of rejecting
the null hypothesis when it is really true
 The guide provided by the statistical theory is
that this probability must be ‘small’.
 Traditionally
 α = 0.05 is selected for consumer research projects
 α = 0.01 for quality assuranceand
 α = 0.10 for political polling

11. Critical Region or Rejection Region
 The rejection region is the range of sample
statistic values within which if values of the
sample statistic falls (i.e. outside the limits of
the acceptance region), then null hypothesis is
rejected.
 The value of the sample statistic that separates the
regions of acceptance and rejection is called
critical value.

12. Formulate a Decision Rule to
Accept Null Hypothesis
 Compare the calculated value of the test statistic with
the critical value (also called standard table value
of the test statistic).
 The decision rules for null hypothesis are as
follows:
 Accept H0 if the test statistic value falls within the area of
acceptance, i.e. if
calculated value of a test statistic < criticalvalue
 Reject otherwise