tailieunhanh - A textbook of Computer Based Numerical and Statiscal Techniques part 52

A textbook of Computer Based Numerical and Statiscal Techniques part 52. By joining statistical analysis with computer-based numerical methods, this book bridges the gap between theory and practice with software-based examples, flow charts, and applications. Designed for engineering students as well as practicing engineers and scientists, the book has numerous examples with in-text solutions. | 496 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES The decision rule can be summarized as Reject H0 if the test statistic falls in the critical region Reject H0 if the test statistic is more extreme than the critical value . PROCEDURE FOR TESTING OF HYPOTHESIS 1 Null Hypothesis Set up the Null Hypothesis H0 2 Alternative Hypothesis Set up the Alternative Hypothesis H1. This would decide whether we have to use a one tailed test or two tailed test. 3 Level of Significance Choose the appropriate level of significance a. 4 Test Statistic Compute the test statistic. Z S-Ef under the null Hypothesis 5 Conclusion We compare Z the computed value of Z in above step 4 with the significant value tabulated value Za at the given level of significance a . a If IZ l Za we say that it is not significant . there is no significant difference and we accept H0. b If IZI Za we say that it is significant and the null hypothesis H0 is rejected at level of significance a. STANDARD ERROR The standard error is defined as the standard deviation of the sampling distribution of a statistic. This is denoted by . The standard error . plays a very important role in the large sample theory and forms the basis of the testing of hypothesis. If t is any statistic for large sample. Z t EV . f is normally distributed with N 0 1 . mean 0 and variance unity. For large samples the standard errors of some of the well known statistic are given below. Statistic Standard Error 1. Sample mean x c 4n 2. Observed sample proportion P JPQ n 3. 4. Sample standard deviation S Sample variance S2 c2 2n n 2 n 5. Difference of two sample means xi - x2 Hi2 c 22 y n1 n2 TESTING OF HYPOTHESIS 497 6. Difference of two sample . s S1 - S2 Hi2 Q 22 2n1 2n2 7. Difference of two sample proportions iPiQi P2Q2 n1 n2 Standard error of a statistic may be reduced by increasing the sample size but this results in corresponding increase in cost time labour etc. Now in the similar manner we given below .