Simple Hypothesis: A statistical hypothesis which specifies the population completely (i. e. the form of probability distribution and all parameters are known) is called a simple hypothesis. 1. Composite Hypothesis: A statistical hypothesis which does not specify the population completely (i. e. either the form of probability distribution or some parameters remain unknown) is called a Composite Hypothesis.
Hypothesis Testing or Test of Hypothesis or Test of Significance Hypothesis Testing is a process of making a decision on whether to accept or reject an assumption about the population parameter on the basis of sample information at a given level of significance. Null Hypothesis: Null hypothesis is the assumption which we wish to test and whose validity is tested for possible rejection on the basis of sample information. It asserts that there is no significant difference between the sample statistic (e. . Mean, Standard Deviation(S), and Proportion of sample (p)) and population parameter (e. g. Mean(µ), standard deviation (?), Proportion of Population (P)). Symbol-It is denoted by Ho Acceptance- The acceptance of null hypothesis implies that we have no evidence to believe otherwise and indicates that the difference is not significant. Rejection- The rejection of null hypothesis implies that it is false and indicates that the difference is significant.
Alternative Hypothesis: Alternative hypothesis is the hypothesis which differs from the null hypothesis. It is not tested. Symbol-It is denoted by H1. Acceptance- its acceptance depends on the rejection of the null hypothesis. Rejection- Its rejection depends on the acceptance of the null hypothesis. Level of Significance Level of significance is the maximum probability of rejection the null hypothesis when it is true.
Symbol- it is usually expressed as % and is denoted by symbol ? (called Alpha) Example- 5% level of significance implies that there are about 5 chances in 100 of rejecting the Ho when it is true or in other words , we are about 95% confident that we will make a correct decision. Test Statistic Test statistic refers to a function of sample observations whose computed value determines the final decision regarding acceptance or rejection of null hypothesis (Ho) Test Statistic |Used for | |z-Test |For test of Hypothesis involving large sample i. e. >30 | |t-Test |For test of Hypothesis involving small sample i. e. ?30 and if ? is| | |unknown. | |X2 –Test |For testing the discrepancy between Observed frequencies and | | |expected frequencies, without any reference to population | | |parameter. | |F- Test |For testing the sample variances. | Critical Region or Rejection Region Critical region is the region which corresponds to a pre- determined level of significance.
The set of values of the test statistic which leads to rejection of the null hypothesis is called region of rejection or Critical region of the test. Acceptance region- The set of values of the test statistic which leads to the acceptance of Ho is called region of acceptance. Critical value- Critical value is that value of statistic which separates the critical region from the acceptance region. It lies at the boundary of the regions of acceptance and rejection. Size of Critical Region- The probability of rejecting a true null hypothesis is called as size of critical region.