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Statistics Homework Solutions 156

Statistics Homework Solutions 156 - 156 CHAPTER 6 13.3505...

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156 CHAPTER 6 The expected values are E ij O i O j O , as shown in the following table. 10.2990 13.3505 13.3505 6.9588 9.0206 9.0206 9.7423 12.6289 12.6289 (b) The χ 2 test is appropriate here, since all the expected values are greater than 5. There are 3 1 3 1 4 degrees of freedom. χ 2 3 i 1 3 j 1 O ij E ij 2 E ij 6 4808. From the χ 2 table, P 0 10. A computer package gives P 0 166. There is no evidence that the rows and columns are not independent. 9. (iii) Both row totals and column totals in the observed table must be the same as the row and column totals, respectively, in the expected table. 11. Let p i , i 0 1 9 be he probability that a random digit has the value i . The null hypothesis is H 0 : p i 0 1 for all i . The total number of observations is n 200. The expected values are equal to np i 200 0 1 20. The test statistic is χ 2 21 20 2 20 17 20 2 20 20 20 2 20 18 20 2 20 25 20 2 20 16 20 2 20 28 20 2 20 19 20 2 20 22 20 2 20 14 20 2 20 8. There are 10 1 9 degrees of freedom. From the χ 2 table, P 0 10. A computer package gives P 0 534. There is no evidence that the random number generator is not working properly.
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