PROCEDURE FOR TESTING HYPOTHESIS

PROCEDURE FOR TESTING HYPOTHESIS

1. PROCEDURE FOR TESTING HYPOTHESIS PRESENTED BY SAHANA. B H 1 ST M.Com Under the guidance of Sundar B. N. Asst. Prof. & Course Co-ordinator GFGCW, PG Studies in Commerce Holenarasipura

2. CONTENT Introduction Meaning Steps to be involved in testing of hypothesis Conclusion Bibliography

3. INTRODUCTION Hypothesis testing is an essential procedure in Statistics. A hypothesis test evaluates two Mutually exclusive statements about population To determine which statement is best supported By the sample data.

4. MEANING Hypothesis testing is an act in statistics whereby An analyst test , an assumption regarding a Population parameter. “ A premise or claim that we want to test or investigate”. A Statistical hypothesis is a hypothesis that is testable on the basis of observed data model as realized values taken by a collection of random variables.

5. Steps to be followed Setup null (H0) and alternative (H1) hypothesis Decide the level of significance . Calculate the test statistics. Obtain the tabulated value . Decision.

6. 1.Setup null( H0) and alternative (H1) hypothesis Value Ɵ0 of parameter Ɵ0 Parameter of two population of interest. H0:Ɵ=Ɵ0 and H1:Ɵ≠Ɵ0 ( 2TAILED TEST) H0:Ɵ≤Ɵ0 & H1:Ɵ>Ɵ0 H0:Ɵ≥Ɵ0 & H1: Ɵ<Ɵ0 (1 TAILED TEST) H0:Ɵ1= Ɵ2 & H1 :Ɵ1≠Ɵ2 ( 2 tailed) H0:Ɵ1≤02 &H1:Ɵ1>Ɵ2 H0:Ɵ1≥02 & H1:Ɵ1<Ɵ2 (1 tailed)

7. For example : Null hypothesis Alternative hypothesis H0 is currently accepted value for a papaparameter. Ex; It is believed that a candy machine chocolate bars that are on average 5g. A worker claims that the machine after maintenance no longer makes 5g. Bars. Write H0 and H1. It’s also called research hypothesis it involves the claim to be tested. Denoted as H1. Solution; H0;m is equal to 5g. H1; m is not equal to 5g.

8. 2.Level of significance. Generally alpha is provided in problem of hypothesis. If alpha is not specified then take 5% is usually assumed .(0.05) The significance level for given hypothesis test is a value for which p values less than or equal to considered statistically significant. for example : In an upper tailed z test if a=0.05 than the critical value is z=1.645.

9. Continued- Another interpretation of significance level ‘based in decision theory, is that corresponds to the value for which one chooses to reject or accept the null hypothesis. The probability that this is a mistake – the null hypothesis is true when z statistic-is less than 0.01 in decision theory this is known as type 1 error. The probability of type 1 error is equal to significance level’, the probability of rejecting H0 when it’s fact falls is equal to 1 to minimize the probability of type 1 error , the significance level is generally choosen to be small.

10. 3. Test statistic Formula : Test statistic = sample statistic- parameter/standard error of sample statistic. its also known as calculated value of the test statistic) Ex: the mean life of particular battery is 75hr. A sample of 9 bulbs is chosen and found to have S D.of 10hr”s and mean of 80 hrs . Find test statistic. T= 80-75/10 (9) =5/3.333 Answer:=1.5

11. 4. Critical value It’s a tabulated value of the test statistic which can be obtained from the corresponding standard table. According to given ά and tails of the test. When the sampling distribution of the statistic is normal or nearly normal that critical value can be expressed as a T score or a z score. To find a critical value follow these steps. Compute alpha (a). a=1-(confidence level /100) Find the critical probability (p*)’p*=1-a/2. To express the citical value as a z score, find the z score having a cumulative probability equal to the critical probability (p*).

12. To express the critical value as a t statistic, follow these steps Find the degrees of freedom (df). Often, df is equal to the sample size -1 The critical t statistic (t*) is the t statistic having degrees of freedom equal to do and a cumulative probability equal to the critical probability.

13. 5.Decision The decision can be made by comparing the calculated value and the tabulated value of the test statistic used for the given hypothesis problem. If calculated value lies in the acceptance region then we accept. Calculated value ≤ tabulated value , H0 is accepted.

14. Conclusion Hypothesis testing is a process used to evaluate the strength of Evidence from sample and provides a framework for making Determinations related to the population. Basically an idea that must be put to the test . A research Questions should lead to clear, testable predictions.

15. BIBLIOGRAPHY Procedure of setting null and alternative hypothesis ( retrieved from , https://youtu.be/HTEW4L1iGoM ) Setting of level of significance and other procedure (retrieved from, https://youtu.be/h3U63-P--Y )