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A very important aspect of the sampling theory is the study of the tests of significance, which enable us to decide on the basis of the sample results, if

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  1. The deviation between the observed sample statistic and the hypothetical parameter value, or
  2. The deviation between two independent sample statistics:

Is significant or might be attributed to chance or the fluctuations of sampling is significant or might be attributed to chance or the fluctuations of sampling.

Since, for large n, almost all the distributions, eg., Binomial, Poisson, Negative binomial, Hyper geometric, t, F, chi square can be approximated very closely by a normal probability curve, we use the normal test of significance for large samples. Some of the well known tests of significance for studying such differences for small samples are t-test, F-test and Fisher’s z –transformation.

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