Elementary Statistics and Computer Application

Theory of Testing Hypothesis

Hypothesis

• Hypothesis is a statement or assumption that is yet to be proved.

Statistical Hypothesis

• When the assumption or statement that occurs under certain conditions is formulated as scientific hypothesis, we can construct criteria by which a scientific hypothesis is either rejected or provisionally accepted. For this purpose, the scientific hypothesis is translated into statistical language. If the hypothesis in given in a statistical language it is called a statistical hypothesis.

For eg:-

• The yield of a new paddy variety will be 3500 kg per hectare – scientific hypothesis.
• In Statistical language if may be stated as the random variable (yield of paddy) is distributed normally with mean 3500 kg/ha.

Simple Hypothesis

• When a hypothesis specifies all the parameters of a probability distribution, it is known as simple hypothesis. The hypothesis specifies all the parameters, i.e µ and σ of a normal distribution.

Eg:-

• The random variable x is distributed normally with mean µ=0 & SD=1 is a simple hypothesis. The hypothesis specifies all the parameters (µ & σ) of a normal distributions.

Composite Hypothesis

• If the hypothesis specific only some of the parameters of the probability distribution, it is known as composite hypothesis. In the above example if only the µ is specified or only the σ is specified it is a composite hypothesis.

Null Hypothesis - Ho

• Consider for example, the hypothesis may be put in a form ‘paddy variety A will give the same yield per hectare as that of variety B’ or there is no difference between the average yields of paddy varieties A and B. These hypotheses are in definite terms. Thus these hypothesis form a basis to work with. Such a working hypothesis in known as null hypothesis. It is called null hypothesis because if nullities the original hypothesis, that variety A will give more yield than variety B.The null hypothesis is stated as ‘there is no difference between the effect of two treatments or there is no association between two attributes (ie) the two attributes are independent. Null hypothesis is denoted by Ho.

Eg:-

• There is no significant difference between the yields of two paddy varieties (or) they give same yield per unit area. Symbolically, Ho: µ1=µ2.

Alternative Hypothesis

• When the original hypothesis is µ1>µ2 stated as an alternative to the null hypothesis is known as alternative hypothesis. Any hypothesis which is complementary to null hypothesis is called alternative hypothesis, usually denoted by H1.

Eg:-

• There is a significance difference between the yields of two paddy varieties. Symbolically,
• H1: µ1≠µ2 (two sided or directionless alternative)
• If the statement is that A gives significantly less yield than B (or) A gives significantly more yield than B. Symbolically,
• H1: µ1 < µ2 (one sided alternative-left tailed)
• H1: µ1 > µ2 (one sided alternative-right tailed)

Testing of Hypothesis

• Once the hypothesis is formulated we have to make a decision on it. A statistical procedure by which we decide to accept or reject a statistical hypothesis is called testing of hypothesis.