Statistics Homework Solutions 212

Statistics Homework Solutions 212 - 212 CHAPTER 9(c The...

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Unformatted text preview: 212 CHAPTER 9 (c) The Bonferroni method is more powerful, because it is based on the actual number of comparisons being made, which is 7. The Tukey-Kramer method is based on the largest number of comparisons that could be made, which is 7 8 2 28. ¡ £¤ ¥ ¦¥ ¤ 5. (a) t16 025 6 3 0083 (the value obtained by interpolating is 3.080). The value of MSE is 2.3023. The 5% critical value is therefore 3 0083 2 2 3023 5 2 8869. We may conclude that the mean for 750 C differs from the means for 850 C and 900 C, and that the mean for 800 differs from the mean for 900 C. ¨ ¡ £ ©¥ ¨ ¨ ¤ ¡ ¦ ¡ ¨ (b) q4 16 05 4 05. The value of MSE is 2.3023. The 5% critical value is therefore 4 05 2 3023 5 2 75. We may conclude that the mean for 750 C differs from the means for 850 C and 900 C, and that the mean for 800 differs from the mean for 900 C. ¨ ¡ £ ¨ ¨ ¨ ¡ ¡ ¡ (c) The Tukey-Kramer method is more powerful, because its critical value is smaller. 7. (a) t16 025 3 2 6730 (the value obtained by interpolating is 2.696). The value of MSE is 2.3023. The 5% critical value is therefore 2 6730 2 2 3023 5 2 5651. We may conclude that the mean for 900 C differs from the means for 750 C and 800 C. ¨ ¡ £ ©¥ ¨ 2 75. We ¡ 2 3023 5 ¨ £ ¨ ¨ ¤ ¡ ¦ ¡ ¨ (b) q4 16 05 4 05. The value of MSE is 2.3023. The 5% critical value is therefore 4 05 may conclude that the mean for 900 C differs from the means for 750 C and 800 C. ¨ ¨ ¡ ¡ ¡ (c) The Bonferroni method is more powerful, because its critical value is smaller. 2 012, MSE 0 22815, the sample sizes are 16 and 9. The sample means are X 1 1 255625, 1 756667. The 95% confidence interval is 0 501042 2 012 0 22815 1 16 1 9 , or 0 1006 0 9015 . ¨ ¨ ¡  ¨ ¤ ¥ £ ¢ £¤ ¨ ¨ ¨ ¡ ¨ 025 ¥ ¡ ¨ ¨ ¡ 9. (a) t47 X2 ¡ (b) The sample sizes are J1 16, J2 9, J3 14, J4 12. MSE 0 22815. We should use the Studentized range value q4 47 05. This value is not in the table, so we will use q4 40 05 3 79, which is only slightly larger. The values of q4 40 05 MSE 2 1 Ji 1 J j are presented in the table on the left, and the values of the differences X i X j are presented in the table on the right. ¨ ¡ ¡ ¡ ¥ 2 0 50104 0 0 33881 0 31750 3 0 16223 0 33881 0 0 02131 4 0 18354 0 3175 0 02131 0 ¨ ¨ ¨ ¨ ¨ ¨ ¨ 1 0 0 50104 0 16223 0 18354 ¨ 1 2 3 4 ¨ ¡ ¡ ¨ ¨ £ ¢ 4 0.48884 0.56446 0.50358 ¨ ¡ ¡ £ ¦¥ ¤ £ ¤ ¡ 0.50358 ¡ ¡ ¡ ¡ ¡ ¡ ¡ 0.54691 0.56446 3 0.46846 0.54691 ¡ ¡ 0.53336 0.46846 0.48884 2 0.53336 ¨ 1 1 2 3 4 None of the differences exceeds its critical value, so we cannot conclude at the 5% level that any of the treatment means differ. 11. (a) t8 025 2 306, MSE 1 3718. The sample means are X 1 1 998 and X 3 5 300. The sample sizes are J1 5 and J3 3. The 95% confidence interval is therefore 3 302 2 306 1 3718 1 5 1 3 , or 1 330 5 274 . ¡ ¨ ¥ ¨  ¨ ¤ ¥ £ ¢ £¤ ¡ ¨ ¨ ¨ ¡ ¨ ¨ ¡ ¨ ¡ ¡ ¡ ...
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