Basics of testing of hypothesis.

1. TESTING OF HYPOTHESIS
HAFIS HAKKIM A

2. HYPOTHESIS TESTING
Hypothesis testing is a statistical method to evaluate or
investigate the validity of a claim or assumption about
something based on sample data.

3. SIMPLE AND COMPOSITE HYPOTHEIS
• Simple hypothesis
If the hypothesis specifies population parameter completely. It is called simple
hypothesis.
• Composite Hypothesis
If the hypothesis doesn’t specifies population parameter completely. It is called
composite hypothesis.

4. HYPOTHESIS
• A hypothesis is some statements about the
characteristics of a population.
The average weight of students in a college,
for instance, is 50kg.
There are two types of hypothesis
1. Null Hypothesis
2. Alternative Hypothesis

5. NULL HYPOTHESIS AND ALTERNATIVE
HYPOTHESIS
• Null Hypothesis:
It is the hypothesis that is to be tested. It is denoted by 𝐻0
• Alternative Hypothesis:
It is the Hypothesis that in some sense contradicts the null
hypothesis. It is denoted by 𝐻𝐴 𝑜𝑟 𝐻1
Remarks:
Researchers always try to reject the null hypothesis to
establish something novel.

6. EXAMPLE
• Previously, people believed that the sun is rotating around the Earth until Galileo,
an Italian astronomer, proved through his observations that the Earth is actually
revolving around the sun. This discovery challenged the widely accepted belief of
geocentrism, which people used to believe for centuries.
• Here previously believed theory (the Sun is rotating around the Earth) is the Null
Hypothesis and the theory Galileo wanted to prove (Earth is rotating around the
Sun) is the Alternative Hypothesis. Here the test or observation Galileo perform can
be called a Hypothesis testing.

7. • Let’s say for a particular candy manufacturing company, it is believed that a candy
machine makes chocolate bars that are an average of 5 grams. That candy
manufacturing plant has been making chocolate bars for 10 years now suddenly a
worker claims that the machine no longer makes 5 grams of each chocolate bar. So is
the worker wrong or the machine is not functioning properly?
• To answer those questions the owner of that candy company should perform
Hypothesis testing.
• Here the Null Hypothesis is the statement “The machine is functioning correctly
and making each chocolate bar 5 grams” and the alternative hypothesis is the
statement of the worker “The machine no longer makes 5 grams of each chocolate
bar”. 𝐻0: 𝜇 = 80
𝐻1: 𝜇 ≠ 80
EXAMPLE

8. EXAMPLE
• Statement: Mean Blood Sugar Level in India is 80 mg/dL
The Mean is
80mg/dL
The Mean is
not 80mg/dL
Null
Hypothesis
Alternative
Hypothesis
𝐻
1
𝐻0: 𝜇 = 80
𝐻1: 𝜇 ≠ 80

9. TYPES OF ERRORS
𝐻0 is accepted when
𝐻0 is true
(No Error)
𝐻0 is accepted when
𝐻1 is true
(Type II error)
𝐻0 is rejected when
𝐻0 is true
(Type I error)
𝐻0 is rejected when
𝐻1 is true
(No Error)
Decision
Accept 𝐻0
Reject 𝐻0
State of nature
𝐻0 is true 𝐻1 is true

10. • The probability of type I Error is denoted by 𝛼
• The probability of type II Error is denoted by β
• i.e.
𝛼=P(type I Error)=P(Rejecting 𝐻0 when 𝐻0 is true)
β=P(type II Error)= P(Accepting 𝐻0 when 𝐻1 is true)

11. POWER OF THE TEST
• Probability of rejecting 𝐻0 when 𝐻1is true is called the
power of the test.
Power=P(rejecting 𝐻0 when 𝐻1is true )
=1-P(Accept 𝐻0 when 𝐻1is true)
=1-P(Type II Error)
=1- β

12. LEVEL OF SIGNIFICANCE (𝛼)
• The probability of type I Error is called level of significance.
𝛼=P(type I Error)=P(Rejecting 𝐻0 when 𝐻0 is true)

13. CRITICAL REGION
The region in which the Null Hypothesis 𝐻0 is rejected is
called critical region or rejection region

14. ACCEPTANCE REGION
• The region in which 𝐻0 is accepted is called acceptance
region.

15. TEST STATISTIC
• The test statistic is a random variable whose value is
calculated from the sample data. Its value determines
either to accept or to reject the null hypothesis 𝐻0.

16. ONE TAILED AND TWO TAILED TEST
• Test of hypothesis in which alternative hypothesis involves
a sign > or < is called one tailed test. In which the critical
region will be either in left side or right side.
• Test of hypothesis in which alternative hypothesis involves
a sign ≠ is called two tailed test. In which critical region will
be in both tails.

18. PROCEDURE OF HYPOTHESIS TESTING

19. • Step 1
Set up the Null Hypothesis 𝐻0 and Alternative Hypothesis 𝐻1.
• Step 2
Set up a suitable level of significance (α )
• Step 3
Identify the test statistic and its probability distribution.
• Step 4
Determine acceptance region and critical region
• Step 5
Calculate the value of test statistic
• Step 6
If the calculated value of test statics fall in the critical region reject the null hypothesis 𝐻0,
otherwise accept it.
i.e; if the calculated value exceeds the table value reject the 𝐻0 otherwise accept it.

20. CRITICAL VALUE
• The value of test statistic which seperates the critical region and acceptance region
is called critical value.

21. THANK YOU
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