The process of accepting rejecting a statistical hypothesis based on sampling is called testing of hypothesis.
Eg: The Hypothesis 5% of people in a city A-Are suffering from TB is a Statistical Hypothesis.
Taking a random sample of the size n from the population of the city, calculating the proportion of the individuals suffering from TB and deciding whether we have to accept or reject the hypothesis is called Statistical Test .
The standard deviation of a statistic is called standard error of statistic.
Let X1,X2 etc be the means of possible samples of size n drawn from a population, the standard deviation of the sample ,means the standard error of these means. This is found to be / n, where is the population standard deviation and n is the sample size.
The number of degrees of freedom in a problem, distribution, etc., is the number of parameters which may be independently varied . It is the no of independent observations in a set’
If we are choosing any 5 nos. , whose total is 100, we can exercise our independent choice for any 4 nos. Only the 5 th no. is fixed by virtue of the total being 100. In this example there is only 1 restriction in our freedom. Therefore the degrees of freedom is 4.
A statistic (singular) is the result of applying a statistical algorithm to a set of data . In the calculation of the arithmetic mean , for example, the algorithm directs us to sum all the data values and divide by the number of data items. In this case, we call the mean a statistic.
The critical region CR , or rejection region RR , is a set of values of the test statistic for which the null hypothesis is rejected in a hypothesis test; that is, the sample space for the test statistic is partitioned into two regions; one region (the critical region) will lead us to reject the null hypothesis H 0 ', the other not. So, if the observed value of the test statistic is a member of the critical region, we conclude 'reject H 0 '; if it is not a member of the critical region then we conclude 'do not reject H 0 .