.
Chi-square Distribution
I I df\\area .995
11 lo.00004
I .990
lo.00016
I .975
lo.00098
I .950
lo.00393
I I .900
.750
10.01579 lo.10153
I .500
lo.45494
I I I I I I .250
.100
.050
.025
.010
.005
11.32330 12,70554 13.84146 15.02339 16.63490 17.87944
I 2 lo.01003 10.02010 lo.05064 lo.10259 jo.21012 lo.57536 11.38629 12.77259 14.60517 15.99146 17.37776 19.21034 110.59663
I
I
I 3 !I 0.01112 lo.11483 lo.21580 lo.35185 !o.58437 11.21253 12.36597 14.10834 16.25139 17.81473 19.34840 111.34487112.83816
1410.20699
I
lo.29111 lo.48442 10.71072 11.06362 11.92256 13.35669 15.38527 17.77944 19.48773 111.14329113.27670 114.86026
I
I
5
I6
10,41174 lo.55430 lo.83121 11.14548 11.61031 12.67460 14.35146 16.62568 19.23636 111.01050112.83250115.08621 !16.74960
10.67573 lo.87209 11.23734 11.63538 12.20413 13.45460 15.34812 17.84080 110.64464 112.59159 114.44938 116.81189 118.54758
I7
II 8
I9
I
I
10
lo.98926 11.23904 11.68987 12.16735 12.83311 14.25485 16.34581 19.03715 112.01704 114.06714 116.01276 118.47531 120.27774
I
jl.34441
I
il.73493
i
11.64650 12.17973 12.73264 13.48954 15.07064 17.34412 110.21885113.36157 115.50731117.53455120.09024121.95495
I
12.08790 12.70039 13.32511 14.16816 15.89883 18.34283 111.38875 114.68366116.91898l19.02277121.66599123.58935
I
12.15586 12.55821 13.24697 13.94030 J4.86518 16.73720 19.34182 112.54886115.98718118.30704120.48318123.20925125.18818
~12.60322
13.05348 13.81575 14.57481 15.57778 17.58414 110.34100113.70069 117.27501119.67514121.92005 124.72497 126.75685
~13.07382
13.57057 14.40379 15.22603 16,30380 18.43842 111.34032 114.84540 118.54935 121.02507 123.33666 l26.21697 128.29952
II
I
13
13.56503 14.10692 15.00875 15.89186 17.04150 19.29907 112.33976j15.98391119.81193 122.36203 J24.73560121.68825 129.81947
~!
14.07467 14,66043 15.62873 16.57063 17,78953 110.16531 113.33927 ,17.11693 121.06414 123.68479 126.11895 129.14124 131.31935
II 15
I 16
!4.60092 15.22935 16.26214 17.26094 !8.s4676 111.03654 J14.33886 118.24509 122.30713 124.99579 127.48839 130.57791 132.80132
I
I
/5_14221 15.81221 16.90766 17.96165 19.31224 111.91222 115.33850 J19.36886123.54183 126.29623 l28.84535131.99993 134.26719
I
~15.69722
16.40776 17.56419 18.67176 110.08519 112.79193 116.33818 120.48868124.76904127.58711130.19101133.40866135.71847
~16,26480
17.01491 18.23075 19,39046 110.86494 113.67529117.33790 121.60489125.98942 128.86930 131.52638 134.80531 137.15645
~16.84397
17.63273 18.90652 110.11101 111.65091 114.56200118.33765 122.71781127.20357 130.14353 132.85233136.19087 138.58226
I 20
II 21
l
I
22
II 23
17.43384 18.26040 19.59078 110.85081 )12.44261 115.45177119.33743 123.82769128.41198131.41043 134.16961137.56623 139.99685
18.03365 18.89720 110.28290 111.59131113.23960116.34438120.33723 124.93478129.61509132.67057135.47888138.93217 ,41.40106
18.64272 19.54249 110.98232 112.33801 114.04149 117.23962 l21.33704l26.03927130.81328133.92444136.78071140.28936 142.79565
I!9.26042 110.19572 111.68855 113.09051 114.84796118.13730122.33688127.14134132.00690135.17246138.07563
141.63840144.18128
~,9.88623
110.85636 112.40115 113.84843 l15.65868 119.03725 123.33673 128.24115 133.19624 136.41503 139.36408 142.97982 145.55851
I 25 ,10.51965 111.52398 113.11972 114.61141 116.47341 119.93934124.33659129.33885134.38159137.65248 140.64647 144.31410 146.92789
~111.16024112.19815
113.84390 115.37916111.29188 J20.84343 125.33646130.43457135.56317 138.88514141.92317 J45.64168148.28988
I 27
I 28
/11.80759112.87850114.57338116.15140,18.11390121.74940126.33634131.52841136.74122140.11327143.19451146.96294149.64492
/12.45134 113.56471 115.30786 116.92788 118.93924 122.65716 127.33623 132.62049137.91592 J41.33714 144.46079 148.27824 j5o.99338
~113.12115
114.25645 116.04707 117.70837 119.76774123.56659128.33613 133.71091139.08747142.55697 145.72229 149.58788 ,52.33562
~113.78672
114.95346 116.79077 118.49266 !20.s9923 124.47761129.33603 134.79974140.25502 143.77297146.9792415o.89218 153.67196
9