hw2_solutions

hw2_solutions - STAT 3022, February 12, 2009 TA: Jinghan...

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Unformatted text preview: STAT 3022, February 12, 2009 TA: Jinghan Meng Homework 2 Solutions EX 7.22 (a) df = n- 1 = 114 (b) Using Table D, we refer to df = 100. Because 1 . 290 < | t | < 1 . 660, the p-value is . 05 < P < . 10. (c) Use the following R command to compute p-value: > pt(-1.55,114) [1] 0.06195664 So the p-value is 0.0619. EX 7.26(R) (a) Use a histogram or stemplot to examine the distribution of the CRP data. > CRP <- c(0.00, 3.90, 5.64, 8.22, 0.00, 5.62, 3.92, 6.81, 30.61, 0.00, 73.20, 0.00, 46.70, 0.00, 0.00, 26.41, 22.82, 0.00, 0.00, 3.49, 0.00, 0.00, 4.81, 9.57, 5.36, 0.00, 5.66, 0.00, 59.76, 12.38, 15.74, 0.00, 0.00, 0.00, 0.00, 9.37, 20.78, 7.10, 7.89, 5.53) > hist(CRP) > stem(CRP) The decimal point is 1 digit(s) to the right of the | 0 | 000000000000000034455666677889 1 | 026 2 | 136 3 | 1 4 | 7 5 | 6 | 0 7 | 3 1 STAT 3022, February 12, 2009 TA: Jinghan Meng Histogram of CRP CRP Frequency 20 40 60 80 5 10 15 20 25 30 The distribution is sharply right-skewed, with two or three high outliers. (b) Means are typically not the best measure of center for skewed distributions. (c) A 95% confidence interval for the mean is given by the following R command: > t.test(CRP) One Sample t-test data: CRP t = 3.8308, df = 39, p-value = 0.0004526 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 4.735093 15.329407 sample estimates: mean of x 10.03225 2 STAT 3022, February 12, 2009 TA: Jinghan Meng So the 95% confidence interval is [4 . 735 , 15 . 329]. The skewness of the distribution makes this methodology somewhat suspect. EX 7.32(R) (a) > before <- c(55.7, 54.9, 59.6, 62.3, 74.2, 75.6, 70.7, 53.3, + 73.3, 63.4, 68.1, 73.7, 91.7, 55.9, 61.7, 57.8) > after <- c(61.7, 58.8, 66.0, 66.2, 79.0, 82.3, 74.3, 59.3, + 79.1, 66.0, 73.4, 76.9, 93.1, 63.0, 68.2, 60.3) > change <- after - before > change [1] 6.0 3.9 6.4 3.9 4.8 6.7 3.6 6.0 5.8 2.6 5.3 3.2 1.4 7.1 6.5 2.5 The weight change for each subject is given above....
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This note was uploaded on 02/24/2011 for the course STAT 3022 taught by Professor Staff during the Spring '08 term at Minnesota.

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hw2_solutions - STAT 3022, February 12, 2009 TA: Jinghan...

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