Testing of Hypothesis - Introduction

 

Inferential Statistics

Definitions:

Hypothesis: Hypothesis is a statement about the values of the population parameter. It is made on the basis of the information obtained by experimentation.

Testing of hypothesis is a procedure for deciding whether to accept or reject the hypothesis. Procedures which enable us to decide whether to accept or reject hypothesis are called tests of hypothesis, also known as test of significance. 

Statistical hypothesis: a statistical hypothesis is a statement about the parameters of one or more populations.

Example:

(i) The average IQ of normal human beings is 113.

(ii) The teaching methods in both the schools are effective.

There are two types of hypotheses. They are Null hypothesis and alternative hypothesis.

Null hypothesis:

A null hypothesis is a statistical hypothesis formulated for the sole purpose of rejecting it.

Example: if we wish to decide whether one procedure is better than the other, then we formulate the null hypothesis the null hypothesis as there is no difference between the procedures.

Generally null hypothesis is denoted by H_0.

Alternative hypothesis:

An alternative hypothesis is any statistical hypothesis that differs from a given null hypothesis.

Example: If null hypothesis; H₀: µ = 20

Then alternative hypothesis denoted by H₁ or H_a is H₁: µ≠20.

The alternative hypothesis, H₁: µ≠20 is known as two (tailed) sided alternative hypothesis.

Level of Significance (   The probability of Type I error is called the level of significance.

In other words, the maximum probability with which we would be willing to risk a type I error is called the level of significance. This probability, denoted by α, in practice a level of significance of 0.05 and 0.01 is customary, although other values are used.

Type I error: Rejecting the null hypothesis H₀ when it is true is defined as type I error and is denoted by α

Type II error: Accepting the null hypothesis H₁ when it is false is defined as type II error and is denoted by (1- α) i.e., β.