Statistics Homework Solutions 156

Statistics Homework Solutions 156 - 156 CHAPTER 6 £ ¡...

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Unformatted text preview: 156 CHAPTER 6 £ ¡ 13.3505 9.0206 12.6289 O , as shown in the following table. j 10.2990 6.9588 9.7423 Oi O The expected values are Ei j 13.3505 9.0206 12.6289 (b) The χ2 test is appropriate here, since all the expected values are greater than 5. 4 degrees of freedom. Ei j £¥ Ei j 2 6 4808. ¡ 1 0 166. ¡ ¡ ¨ ¤ ¡ ¤ ¡ 0 10. A computer package gives P ¨ ¤¥ ∑ 3 1 ∑ 3 1 Oi j j i 2 table, P From the χ ¨ 13 ¡ χ2 ¡ §¥ There are 3 ¡ There is no evidence that the rows and columns are not independent. 9 be he probability that a random digit has the value i. The null hypothesis is H0 : pi 20. 25 20 2 20 £¥ ¤ ¢ 2 01 ¢ 200 0 1 ¡ 20 20 17 20 20 20 20 20 18 20 20 20 19 20 2 20 22 20 2 20 14 20 2 20 8. £¥ ¤ ¡ ¢ £¥ ¤ £¥ ¡ ¤ ¢ ¢ £¥ ¤¢ £¥ ¡ ¤ ¡ ¢ £¥ ¤¢ £¥ ¡ ¡ £¥ ¤ ¡ ¡ ¤ 9 degrees of freedom. 0 10. A computer package gives P 0 534. ¡ ¡ £¥ ¡ table, P ¨ ¢ 1 2 ¡ ¡ ¨ ¤ ¡ From the χ2 20 2 2 ¡ There are 10 21 200. The expected values are equal to np i ¡ The test statistic is 16 20 2 20 28 2 ¤ ¡ χ2 ¡¥¨  The total number of observations is n ¡ 01 ¨¨¨  Let pi , i for all i. ¡ 11. (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. ¨ 9. There is no evidence that the random number generator is not working properly. 217 and O2 210. The column totals are O 1 32, O 2 15, O 3 37, O 4 38, 46, O 8 42, O 9 34, O 10 36, O 11 28, O 12 26. The grand total is O 427. ¡ ¡ ¡ ¡ ¡ ¡ O , as shown in the following table. £ 4 19.31 18.69 5 22.87 22.13 Month 6 7 24.39 23.38 23.61 22.62 8 21.34 20.66 9 17.28 16.72 10 18.30 17.70 11 14.23 13.77 ¡ 11 degrees of freedom. 41 33. 21 ¨ ¡ ¡ §¥ £¥ 0 005. A computer package gives P 10 5. ¡ Ei j ¨ 2 ¡ 3 18.80 18.20 ¡ ¡ ¡ ¤¥ ¡ ¨ ¡ ¡ ¤ ¡ ¤ table, P Ei j ¡ Oi j ¡ From the χ2 1 ¡ 1 12 ∑2 1 ∑12 1 i j χ2 ¡ There are 2 Known Unknown 2 7.62 7.38 j 1 16.26 15.74 Oi O The expected values are Ei j ¡ The row totals are O1 O 5 45, O 6 48, O 7 ¡ 13. We can conclude that the proportion of false alarms whose cause is known differs from month to month. 12 13.21 12.79 ...
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