TAILIEUCHUNG - A textbook of Computer Based Numerical and Statiscal Techniques part 55

A textbook of Computer Based Numerical and Statiscal Techniques part 55. 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. | 526 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES 50 x 225 100 Since n is large the test statistic is Z 72 - 42 -1 N 0 1 Now Z V225 - V99 15 - Since Z 3 it is significant at all levels of significance and hence H0 is rejected and we conclude that o A 10. Example 2. It is believed that the precision as measured by the variance of an instrument is no more than . Write down the null and alternative hypothesis for testing this belief. Carry out the test at 1 level given 11 measurements of the same subject on the instrument . 2006 Kanpur 2007 Sol. Null Hypothesis H0 o2 Alternative Hypothesis H o2 Computation of Sample Variance X X - X X - X 2 - - - - - - - X X X - X 2 Under the null hypothesis H0 o2 the test statistic is X nf S X- x 2 o2 o2 which follows x2-distribution with . 11 - 1 10. TESTING OF HYPOTHESIS 527 Since the calculated value of x2 is less than the tabulated value of x2 for 10 . at 1 level of significance it is not significant. Hence H0 may be accepted and we conclude that the data are consistent with the hypothesis that the precision of the instrument is . ii Chi-Square Test of Goodness of Fit x2 test is an approximate test for large values of n. x2 test enables us to ascertain how well the theoretical distributions fit empirical distributions or distribution obtained from sample data. If the calculated value of chi-square is less than the table value at a specified level of significance the fit is considered to be good. Generally we take significance at 5 level. Similarly if the calculated value of x2 is greater than the table value the chi-square fit is considered to be poor. Example 3. The following table shows the distribution of digits in numbers

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