1. TESTING OF HYPOTHESIS

2. What is hypothesis? Hypothesis simply mean assumption or sum supposition to be proved or disproved . Characteristics Of Hypothesis Hypothesis should be clear and precise. Hypothesis should be capable of being tested Hypothesis should state relationship between variables if it happens to be relational Hypothesis. Hypothesis should be limited in scope and must be specific Hypothesis should be in most simple terms Hypothesis should be consistent with most known facts.

3. Statisitcsand :A statistic is a characteristic of a sample,whereas • parameter : parameter is a characteristic of a population

4. Basic concepts concerning testing of hypothesis? Null hypothesis- an initial belief of statement about the population parameter is called null hypothesis.NullHypothesis is generally symbolised as Ho Alternative hypothesis- the hypothesis is complimentary to the null hypothesis is called alternative hypothesis. Alternative hypothesis is usually one which one wishes to prove and the null hypothesis is the one which one wishes to disprove

5. example Suppose we want to test the hypothesis that the population mean (u)is equal to the hypothesised mean (uH0)=100 Null Hypothesis is that the population mean is equal to the hypothesized mean 100 H0 u=uH0=100 Ha u is not equal uH0 Ha:u>uHa Ha:u<uHa

6. Level of significance • It means the researcher is wiling to take risk of rejecting the null hypothesis when it happens to true

7. Type 1 and type 2 error Type 1- when null hypothesis is true we may rejected this is called type 1 error this is denoted by Alfa is also called producer risk. Type 2- when null hypothesis is false we may accepted this called type 2 error this is denoted by beta is also called consumer risk.

9. Procedure of hypothesis testing • Making a formal statement- the step consist is making a formal statement of null hypothesis and also of the alternative hypothesis • Selecting a significance level- the hypothesis are tested on a pre determined level of a significance and as such the same should be specified generally in practice either 5% level or 1% level is adopted for the purposes.

10. Deciding the distribution- after deciding the level of significance, the next step in hypothesis testing is to determine the appropriate sampling distribution. The choice generally remains between normal distribution and t- distribution. • Selecting a random sample and computing an appropriate value- another step is to select a random sample (s) and compute an appropriate value from the sample data concerning the test statistic utilizing the relevant distribution. In another words, draw a sample to furnish empirical data

11. Calculation of the probability- one has then to calculate the probability that the sample result would diverge as widely as it has from expectation. If the null hypothesis were In fact true. • Comparing the probability- in this step we compare the probability thus calculated with the specified value for Alfa the significance level if our calculated value is less or equal than our value of significance level null hypothesis is accepted and if it is greater then our null hypothesis is rejected.

12. Calculation of the probability- one has then to calculate the probability that the sample result would diverge as widely as it has from expectation. If the null hypothesis were In fact true. • Comparing the probability- in this step we compare the probability thus calculated with the specified value for Alfa the significance level if our calculated value is less or equal than our value of significance level null hypothesis is accepted and if it is greater then our null hypothesis is rejected.

13. TESTS OF HYPOTHESES • Parametric tests or standard tests • Non parametric tests

14. PARAMETRIC TESTS Parametric tests usually assume certain properties of the population from which we draw samples. In parametric test we have to make assumptions about the population parameters like mean, variance.

15. Important parametric tests • Z-test • t-test • x square test • F-test

16. Hypothesis testing of mean In Hypothesis testing of mean, mean of the population can be tested from given formula-

17. Hypothesis testing for differences between means In many decision-situations, we may be interested in knowing whether the parameters of two populations are alike or different. For instance, we may be interested in testing whether female workers earn less than male workers for the same job.

18. Hypothesis testing of proportions In hypothesis testing of proportions, proportions can be tested by using probability.

19. Hypothesis testing for difference between proportions if two samples are drawn from different populations, one may be interested in knowing whether the difference between the proportion of successes is significant or not.