This document discusses key concepts and definitions related to hypothesis testing in statistics. It defines population and sample, parameters and statistics, and the standard error of an estimator. It explains the concepts of the null hypothesis (H0) and alternative hypothesis (H1), critical regions, type I and II errors, and the level of significance. It also defines one-sided and two-sided tests, and the p-value used in hypothesis testing. The document provides examples to illustrate these statistical concepts.

1. Savitribai Phule Pune University, Pune
FYBSc (CS)
Paper – II : Continuous Probability Distribution and Testing of Hypothesis (CPDTH)
TOPIC- Concepts and Definitions Relating to Testing of
Hypotheses.
By,
Prof. Shriram Kargaonkar
Asst. Prof. & HOD, Department of Statistics,
NSS Program Officer and Unnat Bharat Abhiyan Coordinator,
MAEER’s MITACSC Alandi, Pune- 412105
Email – snkargaonkar@mitacsc.ac.in
Mobile- 9762003712

2. Introduction
• In Statistics, hypothesis testing refers to analyzing an
assumption about a population parameter.
• It is used to make an educated guess about an
assumption using statistics.
• With the use of sample data, hypothesis testing makes an
assumption about how true the assumption is for the
entire population from where the sample is being taken.
• Any hypothetical statement we make may or may not be
valid, and it is then our responsibility to provide evidence
for its possibility.
In this lecture, I will teach you important definitions relating
to testing of hypothesis.

3. Important Definitions
1. Population and Sample
2. Parameter and Statistics
3. Standard error of estimator.
4. Concept of null hypothesis and alternative hypothesis
(Research hypothesis)
5. Critical region,
6. type I and type II error,
7. level of significance,
8. one sided and two sided tests,
9. Test of hypothesis,
10. p-value.

4. Population and Sample
Population is the colletion of all objects under study OR
It is the totality of all objects under study.
Sample is the representative part of the entire population.
It possess all the characteristics of the population

5. Parameter and Statistic
Parameter:
It is the Statistical measure based on entire population
Information about the population
A population value
The “truth”
Statistic
It is the Statistical measure based on sample observations only.
An estimate of the population value

9. Types of Hypotheses

10. Examples of H0 and H1
Ex 1) Statement/Claim: Average marks of students in a class is 58 out of 100.
Null Hypothesis  H0: μ = 58 Against
Alternative Hypothesis  H1: μ ≠ 58 OR
H1: μ < 58 OR
H1: μ > 58
Ex 2) Statement/Claim: Cities A & B have proportions of Coffee Consumers .
Null Hypothesis  H0: P1 = P2 Against
Alternative Hypothesis  H1: P1 ≠ P2 OR
H1: P1 < P2 OR
H1: P1 > P2

11. Critical region
In the testing of hypotheses, the
set of all possible outcomes of a
statistical test is divided into two
region viz. Rejection Region
(Critical Region) & Acceptance
region.
Critical Region or Rejection region
is the set of outcomes of a
statistical test for which the null
hypothesis is to be rejected i.e
The common decision for these
set of values is to REJECT H0.
Acceptance region is the set of
outcomes of a statistical test for
which the null hypothesis is to be
accepted.

13. Type I and Type II error
Type II Error
 Reject H0, when H0 is true.
 Consumer’s Risk
Type I Error
 Reject H0, when H0 is true.
 Producer’s risk

14. level of significance (α %)
It is defined as the fixed probability of rejecting null hypothesis (H0)
when, it is true.
Thus, level of significance = P[Type I Error]
= P[Reject H0 | H0 True]
It is denoted by α.
The level of significance is the measurement of the statistical
significance.
Usually, α is taken as 1%, 5% or 10 %.
In Case, it is not mentioned, by default it is considered as 5%

15. One sided and two sided tests
(One Tailed and two tailed tests)
 Whether the test is one sided or two sided, totally depends
upon the alternative hypothesis H1 because Null Hypothesis
is the hypothesis of “No difference”.
 If alternative hypothesis, specifies both direction it is called as
two sided test. It contains ‘≠’ in H1
Examples 1) H1: μ ≠ 58 2) H1: P1 ≠ P2
 If alternative hypothesis, specifies only one direction, it is
called as one sided test. It contains either ‘<‘ or ‘>’ in H1.
Examples 1) H1: μ < 58 <------- Left sided test
2) H1: μ > 58 <------- Right sided test

18. General steps for Testing of Hypothesis

19. P-value
The P-value is also known as the
probability value.
It is defined as the probability of getting a
result that is either the same or more
extreme than the actual observations.
The P-value is known as the level of
marginal significance within the hypothesis
testing that represents the probability of
occurrence of the given event.
Interpretation:
If p-value < 0.05 ==> Reject H0 (Accept H1)
If p-value > 0.05 ==> Accept H0