TAILIEUCHUNG - A textbook of Computer Based Numerical and Statiscal Techniques part 56

A textbook of Computer Based Numerical and Statiscal Techniques part 56. 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. | 536 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Similarly we will get b - E b - adn bC c - E c d - E d adbc Substituting in 2 we get 2 ad- bc 2 r 1 1 1 1 v2 111 X N2 E a E b E c E d ad - bc 2 N ad - bc 2 N ad - bc 2 _1_ a b a c 1 I J 1 1 a b b d a c c d b d c d b d a c b d a c a b a c b d a c c d b d c d a b a b a c b d c d N ad - bc 2 a b a c b d c d Example 11. From the following table regarding the colour of eyes of father and son test if the colour of son s eye is associated with that of the father. Eye colour of son Light Not light Eye colour of father Light 471 51 Not light 148 230 Sol. Null Hypothesis H0 The colour of son s eye is not associated with that of the father . they are independent. Under H0 we calculate the expected frequency in each cell as Product of column total and row total whole total TESTING OF HYPOTHESIS 537 . Conclusion At 5 level for 1 . x2 is tabulated value Since tabulated value of x2 calculated value of x2. Hence H0 is rejected. Example 12. The following table gives the number of good and bad parts produced by each of the three shifts in a factory Good parts Bad parts Total Day shift 960 40 1000 Evening shift 940 50 990 Night shift 950 45 995 Total 2850 135 2985 Test whether or not the production of bad parts is independent of the shift on which they were produced. Sol. Null Hypothesis H0 The production of bad parts is independent of the shift on which they were produced. . the two attributes production and shifts are independent. 2 Under H0 2 3 X2 zz i 1 j 1 Calculation of expected frequencies Let A and B be the two attributes namely production and shifts. A is divided into two classes A1 A2 and B is divided into three classes B1 B2 B3. 538 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES A1B1 0 A1 B2 2850 x 1000 - 2 N 2985 A1B2 0 A1 B2 2850 x 990 v 7 7 99A N 2985 . A1B3 0 A1 B3 2850 x 995 N - 2985 950 A2B1 0 A2 B1 _ 135 x 1000 4527 N 2985 A2B2 0 A2 B2 135 x 990 v 7 v 7 AA 777. N .

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