A textbook of Computer Based Numerical and Statiscal Techniques part 54. 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. | 516 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES where X1 be the mean of a sample of size n1 from a population with mean p1 and variance G12- x 2 be the mean of an independent sample of size n2 from population with mean p2 and variance g22. Remarks 1. Under the null hypothesis H0 p1 p2 . there is no significant difference between the sample means therefore G12 g22 g2 . if the sample have been drawn from the populations with common standard deviation g then x 1 - X 2 Z 1 1 G ------ H1 n2 2. If G12 A g22 and G1 and g2 are not known then test statistic estimated from sample values. . X - X 2 Z . pHOSn K n1 J I n2 J 3. If g is not known then its test statistic based on the sample variances is used. n1S12 n2S22 If G1 g2 we use g2 n n to evaluate g. Test statistic Z X1 X2 n1S2 n2S2 1 1 n1 n2 I n1 n2 E Test of Significance for the Difference of standard Deviations If S1 and S2 are the standard deviations of two independent samples then under the null hypothesis H0 G1 g2 the sample . do not differ significantly the test statistic is given by S1 - S2 Z S. E. S1- S2 For large samples but the difference of the sample standard deviation is given by . S1 - S2 G12 G 22 2n1 2n2 Z S1 S2 H12 G 22 2n1 2n2 when g2 and g22 are not known . population . are not known then the test statistic reduces to Z S1 - S2 S1i S y2n1 2n2 TESTING OF HYPOTHESIS 517 Example 25. Intelligence tests were given to two groups of boys and girls Mean . Size Girls 75 8 60 Boys 73 10 100 Examine if the difference between mean scores is significant. Sol. Null hypothesis H0 There is no significant difference between mean scores . 1 x2. H 1 i Under the null hypothesis Z x1 - x2 If St St K n1 n2 75-73 . m ----1--- 60 100 Conclusion As the calculated value of IZ I the significant value of Z at 5 level of significance H0 is accepted. Example 26. The means of two single large samples of 1000 and 2000 members are inches and inches respectively. Can the samples be
