**Null hypothesis and alternative hypothesis:**In the context of statistical analysis, we often talk about null hypothesis and alternative hypothesis.

- If we are to compare method A with method B about its superiority and if we proceed on the assumption that both methods are equally good, then this assumption is termed as the null hypothesis.
- As against this, we may think that the method A is superior or the method B is inferior, we are then stating what is termed as alternative hypothesis.
- The null hypothesis is generally symbolized as H0 and the alternative hypothesis as Ha.

Examples:

1. Null Hypothesis: H0: There is no difference in the salary of factory workers based on gender.

Alternative Hypothesis: Ha: Male factory workers have a higher salary than female factory workers.

2. Null Hypothesis: H0: There is no relationship between height and shoe size.

Alternative Hypothesis: Ha: There is a positive relationship between height and shoe size.

3. Null Hypothesis: H0: Experience on the job has no impact on the quality of a brick mason’s work.

Alternative Hypothesis: Ha: The quality of a brick mason’s work is influenced by on-the-job experience.

Alternative Hypothesis: Ha: Male factory workers have a higher salary than female factory workers.

2. Null Hypothesis: H0: There is no relationship between height and shoe size.

Alternative Hypothesis: Ha: There is a positive relationship between height and shoe size.

3. Null Hypothesis: H0: Experience on the job has no impact on the quality of a brick mason’s work.

Alternative Hypothesis: Ha: The quality of a brick mason’s work is influenced by on-the-job experience.

The null hypothesis and the alternative hypothesis are chosen before the sample is drawn (the researcher

must avoid the error of deriving hypotheses from the data that he collects and then testing the hypotheses from the same data). In the choice of null hypothesis, the following considerations are usually kept in view:

- Alternative hypothesis is usually the one which one wishes to prove and the null hypothesis is the one which one wishes to disprove. Thus, a null hypothesis represents the hypothesis we are trying to reject, and alternative hypothesis represents all other possibilities.
- If the rejection of a certain hypothesis when it is actually true involves great risk, it is taken as null hypothesis because then the probability of rejecting it when it is true is a (the level of significance) which is chosen very small.
- Null hypothesis should always be specific hypothesis i.e., it should not state about or approximately a certain value.

#### The level of significance

The significance level, also known as alpha or Î±, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant. The researcher determines the significance level before conducting the experiment.

The significance level is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis.

#### Decision rule or test of hypothesis:

Given a hypothesis H0 and an alternative hypothesis Ha, we make a rule which is known as decision rule according to which we accept H0 (i.e., reject Ha) or reject H0 (i.e., accept Ha).

#### Type I and Type II errors:

- In the context of testing of hypotheses, there are basically two types of errors we can make.
- We may reject H0 when H0 is true (Type I error ) and we may accept H0 when in fact H0 is not true(Type II error.).
- The former is known as Type I error and the latter as Type II error.
- In other words, Type I error means rejection of hypothesis which should have been accepted and Type II error means accepting the hypothesis which should have been rejected.
- Type I error is denoted by a (alpha) known as a error, also called the level of significance of test; and Type II error is denoted by b (beta) known as b error.

#### two tailed and one tailed test of hypothesis

- A one-tailed test results from an alternative hypothesis which specifies a direction. i.e. when the alternative hypothesis states that the parameter is in fact either bigger or smaller than the value specified in the null hypothesis.
- A two-tailed test results from an alternative hypothesis which does not specify a direction. i.e. when the alternative hypothesis states that the null hypothesis is wrong.

__One-tailed Tests__- A one-tailed test may be either left-tailed or right-tailed.
- A left-tailed test is used when the alternative hypothesis states that the true value of the parameter specified in the null hypothesis is less than the null hypothesis claims.
- A right-tailed test is used when the alternative hypothesis states that the true value of the parameter specified in the null hypothesis is greater than the null hypothesis claims

**Two-tailed Tests**

The main difference between one-tailed and two-tailed tests is that one-tailed tests will only have one critical region whereas two-tailed tests will have two critical regions. If we require a 100(1−Î±) % confidence interval we have to make some adjustments when using a two-tailed test.

The confidence interval must remain a constant size, so if we are performing a two-tailed test, as there are twice as many critical regions then these critical regions must be half the size. This means that when we read the tables, when performing a two-tailed test, we need to consider Î±/2 rather than Î±.

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