Proses pengerjaan | \({A^2} = – N – \frac{S}{N}\) dengan \(S = \sum\limits_{i = 1}^N {(2i – 1)\left[ {\ln F({X_i}) + \ln (1 – {F_{N + 1}}_{ – i})} \right]} \)
\(i\) | \({X_i}\) | \({Z_i}\) | \(\Phi ({Z_i})\) | \(1 – \Phi ({Z_i})\) | Sorted
\(1 – \Phi ({Z_i})\) | \({k_i}\) | 1 | 7 | -1,5774 | 0,0574 | 0,9426 | 0,016 | -6,9929 | 2 | 12 | -1,173 | 0,1204 | 0,8796 | 0,1761 | -11,5609 | 3 | 15 | -0,9303 | 0,1761 | 0,8239 | 0,2995 | -14,7117 | 4 | 19 | -0,6067 | 0,272 | 0,728 | 0,3885 | -15,7319 | 5 | 26 | -0,0404 | 0,4839 | 0,5161 | 0,4119 | -14,3425 | 6 | 27 | 0,0404 | 0,5161 | 0,4839 | 0,4119 | -16,8211 | 7 | 29 | 0,2022 | 0,5801 | 0,4199 | 0,4839 | -16,5156 | 8 | 29 | 0,2022 | 0,5802 | 0,4199 | 0,5161 | -18,0901 | 9 | 30 | 0,2831 | 0,6115 | 0,3885 | 0,728 | -13,758 | 10 | 33 | 0,5258 | 0,7005 | 0,2995 | 0,8239 | -10.4437 | 11 | 38 | 0,9303 | 0,8239 | 0,1761 | 0,8796 | -6,7619 | 12 | 53 | 2,1437 | 0,984 | 0,016 | 0,9426 | -1,7306 | Dengan rata-rata = \(\bar X = 26,5\), standar deviasi
\(s = 12,362\)
\({Z_i} = \frac{{{X_i} – \bar X}}{s}\)
\(\Phi ({Z_i}) = norm.\_dist({Z_i})\)
\({\rm{ }}S = \sum\limits_{i = 1}^N {(2i – 1)\left[ {\ln F({X_i}) + \ln (1 – {F_{N + 1}}_{ – i})} \right]} = \sum\limits_{i = 1}^{12} {{k_i} = – 147,461} \)
\({A^2} = – N – \frac{S}{N}{\rm{ = }} – 12 + \frac{{147,461}}{{12}}\)
\({A^2} = 0,288415\)
\(A = 0,537043\) |