**Hypothesis Testing**

**Testing Simple Hypothesis**:- **Direct verification** or testing is required in the Simple hypothesis. It can be tested either by observation or by experiments

- When direct observation shows that the supposed cause exists where it was thought to exist, we have a direct verification.
- When a hypothesis is verified by an experiment in a laboratory it is called direct verification by experiment.

**Testing Complex Hypothesis:- **A complex hypothesis cannot be tested directly. When the hypothesis is not amenable for direct verification, we have to depend on indirect verification. **Indirect verification** or testing is a process in which certain possible consequences are deduced from the hypothesis and they are then verified directly.

- To test the hypothesis in terms of deduced consequences, it is necessary to collect evidence by selecting or developing data collecting tools to analyze the data collection, and then interpret results in the light of the hypothesis and its deduced consequences.
- The necessary conditions for confirmation are:

(i) all factual evidence collected through tests or other means (tools) should correspond with the deduced consequences;

(ii) the data-collecting tools should take into account all factors and conditions that are suggested by the consequences;

(iii) the consequences are logically deduced from the hypothesis

Lets’s check out this example:- Suppose the researcher wants to test the hypothesis:

** ‘effective college principals will have a higher level of job satisfaction**.

This hypothesis cannot be tested directly by the researcher. He has to proceed indirectly by deducing the consequences that:

*“ineffective college principals will have a low level of job satisfaction as compared to that of effective principals.”*

- In this way, the researcher does not test the hypothesis but tests the deduced consequences of the hypothesis.
- Once all the deduced consequences after testing come out to be true, the hypothesis is confirmed.
- If some of the consequences are true and/or some others are not, the hypothesis needs to be examined afresh.

**Process of Hypothesis Testing**

Testing of a hypothesis is done by using statistical methods. Testing is used to accept or reject an assumption or hypothesis about a random variable using a sample from the distribution.

- The assumption is the
**Null hypothesis (H0 )**, and it is tested against some**A****lternative hypothesis (H1 )**. - Statistical tests of the hypothesis are applied to sample data.
- The procedure involved in testing a hypothesis is

A) select a sample and collect the data.

B) convert the variables or attributes into a statistical form such as mean, and proportion.

C) formulate hypotheses.

D) select an appropriate test for the data such as a t-test, or Z-test.

E) perform computations.

F) finally draw the inference of accepting or rejecting the null hypothesis.

*Let’s try to understand the process of Hypothesis testing with the help of an example :*

Assume that a radio station selects the music it plays based on the assumption that :

*‘the average age of its listening audience is 30 years***.**

To determine whether this assumption is valid, a hypothesis test could be conducted with the null hypothesis as

Null hypothesis (H0): µ = 30 and

Alternative hypothesis as H1: µ ≠ 30.

- Based on a sample of individuals from the listening audience, the sample mean age, ‘X’, can be computed and used to determine whether there is sufficient statistical evidence to reject H0.
- Conceptually, a value of the sample mean that is “close” to 30 is consistent with the null hypothesis, while a value of the sample mean that is “not close” to 30 provides support for the alternative hypothesis.
- What is considered “close” and “not close” is determined by using the sampling distribution of ‘X’?
- Ideally, the hypothesis-testing procedure leads to the acceptance of H0 when H0 is true and the rejection of H0 when H0 is false.
- Unfortunately, since hypothesis tests are based on sample information, the possibility of errors must be considered.