The technique of randomization used for the selection of sample units makes the test of significance valid for us, for applying the test of significance we first set up a hypothesis a definite statement about the population parameter. Such a hypothesis, which is usually a hypothesis of no difference is called null hypothesis and is usually denoted by H0. According to Prof. R.A.Fisher, null hypothesis is the hypothesis which is tested for possible rejection under the assumption that it is true.

For example, in case of a single statistic, H0 will be that the sample statistic does not differ significantly from the hypothetical parameter values and in the case of two statistics, H0 will be that the sample statistics do not differ significantly.

Having set up the null hypothesis we compute the probability p that the deviation between the observed sample statistic and the hypothetical parameter value might have occurred due to fluctuations of sampling. If the deviation comes out to be significant, null hypothesis is rejected at the particular level of significance adopted and if the deviation is not significant, null hypothesis may be retained at that level.

Any hypothesis which is complementary to the null hypothesis is called an alternative hypothesis, usually denoted by H1. For example, if we want to test the null hypothesis that the population has a specified mean μ0, that is H0: μ = μ0, then the alternative hypothesis could be

- H1: μ ≠ μ0
- H1: μ > μ0
- H1: μ < μ0

The alternative hypothesis in (i) is known as a two tailed alternative and the alternative in (ii) and (iii) are known as right tailed and left-tailed alternatives respectively. The setting of alternative hypothesis is very important since it enables us to decide whether we have to use as single-tailed or two tailed test.

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- Procedure for testing of hypothesis
- Test Of Significance For Large Samples
- Sampling Of Attributes
- Test of significance for difference of proportions
- Sampling of Variables
- Standard Error Of Sample Mean
- Test Of Significance For Single Mean
- Test Of Significance For Difference Of Means
- Test Of Significance For The Difference Of Standard Deviations

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