Mathematical Methods for Physics and Engineering - Matematica.NET

STATISTICSC n (t) 0.5 0.6 0.7 0.8 0.9 0.950 0.975 0.990 0.995 0.999n =1 0.00 0.33 0.73 1.38 3.08 6.31 12.7 31.8 63.7 318.32 0.00 0.29 0.62 1.06 1.89 2.92 4.30 6.97 9.93 22.33 0.00 0.28 0.58 0.98 1.64 2.35 3.18 4.54 5.84 10.24 0.00 0.27 0.57 0.94 1.53 2.13 2.78 3.75 4.60 7.175 0.00 0.27 0.56 0.92 1.48 2.02 2.57 3.37 4.03 5.896 0.00 0.27 0.55 0.91 1.44 1.94 2.45 3.14 3.71 5.217 0.00 0.26 0.55 0.90 1.42 1.90 2.37 3.00 3.50 4.798 0.00 0.26 0.55 0.89 1.40 1.86 2.31 2.90 3.36 4.509 0.00 0.26 0.54 0.88 1.38 1.83 2.26 2.82 3.25 4.3010 0.00 0.26 0.54 0.88 1.37 1.81 2.23 2.76 3.17 4.1411 0.00 0.26 0.54 0.88 1.36 1.80 2.20 2.72 3.11 4.0312 0.00 0.26 0.54 0.87 1.36 1.78 2.18 2.68 3.06 3.9313 0.00 0.26 0.54 0.87 1.35 1.77 2.16 2.65 3.01 3.8514 0.00 0.26 0.54 0.87 1.35 1.76 2.15 2.62 2.98 3.7915 0.00 0.26 0.54 0.87 1.34 1.75 2.13 2.60 2.95 3.7316 0.00 0.26 0.54 0.87 1.34 1.75 2.12 2.58 2.92 3.6917 0.00 0.26 0.53 0.86 1.33 1.74 2.11 2.57 2.90 3.6518 0.00 0.26 0.53 0.86 1.33 1.73 2.10 2.55 2.88 3.6119 0.00 0.26 0.53 0.86 1.33 1.73 2.09 2.54 2.86 3.5820 0.00 0.26 0.53 0.86 1.33 1.73 2.09 2.53 2.85 3.5525 0.00 0.26 0.53 0.86 1.32 1.71 2.06 2.49 2.79 3.4630 0.00 0.26 0.53 0.85 1.31 1.70 2.04 2.46 2.75 3.3940 0.00 0.26 0.53 0.85 1.30 1.68 2.02 2.42 2.70 3.3150 0.00 0.26 0.53 0.85 1.30 1.68 2.01 2.40 2.68 3.26100 0.00 0.25 0.53 0.85 1.29 1.66 1.98 2.37 2.63 3.17200 0.00 0.25 0.53 0.84 1.29 1.65 1.97 2.35 2.60 3.13∞ 0.00 0.25 0.52 0.84 1.28 1.65 1.96 2.33 2.58 3.09Table 31.3 The confidence limits t of the cumulative probability functionC n (t) for Student’s t-distribution with n degrees of freedom. For example,C 5 (0.92) = 0.8. The row n = ∞ is also the corresponding result for thestandard Gaussian distribution.where t crit satisfies C N−1 (t crit )=α/2. Thus the required confidence interval is¯x −√ t crits< µ < ¯x + √ t crits.N − 1 N − 1Hence, in the above example, the 90% classical central confidence interval on µis0.49