Теор.вероятн. и матем.стат / Пр.2 ТВиМС,альб.табл

Таблица 4. Критические значения для χ²-распределения: значения χ_α², удовлетворяющие равенству

, где p_ν(x) – плотность хи-квадрат распределения с ν степенями свободы

ν \ α	0,001	0,005	0,01	0,02	0,05	0,10	0,20	0,30	0,40	0,50	0,60	0,70	0,80	0,85	0,90	0,95	0,99	0,999
1	10,828	7,879	6,635	5,412	3,841	2,706	1,642	1,074	0,708	0,455	0,275	0,148	0,064	0,036	0,016	0,004	0,0002	0,0000
2	13,816	10,597	9,210	7,824	5,991	4,605	3,219	2,408	1,833	1,386	1,022	0,713	0,446	0,325	0,211	0,103	0,0201	0,0020
3	16,266	12,838	11,345	9,837	7,815	6,251	4,642	3,665	2,946	2,366	1,869	1,424	1,005	0,798	0,584	0,352	0,115	0,024
4	18,467	14,860	13,277	11,668	9,488	7,779	5,989	4,878	4,045	3,357	2,753	2,195	1,649	1,366	1,064	0,711	0,297	0,091
5	20,515	16,750	15,086	13,388	11,070	9,236	7,289	6,064	5,132	4,351	3,655	3,000	2,343	1,994	1,610	1,145	0,554	0,210
6	22,458	18,548	16,812	15,033	12,592	10,645	8,558	7,231	6,211	5,348	4,570	3,828	3,070	2,661	2,204	1,635	0,872	0,381
7	24,322	20,278	18,475	16,622	14,067	12,017	9,803	8,383	7,283	6,346	5,493	4,671	3,822	3,358	2,833	2,167	1,239	0,598
8	26,124	21,955	20,090	18,168	15,507	13,362	11,030	9,524	8,351	7,344	6,423	5,527	4,594	4,078	3,490	2,733	1,646	0,857
9	27,877	23,589	21,666	19,679	16,919	14,684	12,242	10,656	9,414	8,343	7,357	6,393	5,380	4,817	4,168	3,325	2,088	1,152
10	29,588	25,188	23,209	21,161	18,307	15,987	13,442	11,781	10,473	9,342	8,295	7,267	6,179	5,570	4,865	3,940	2,558	1,479
11	31,264	26,757	24,725	22,618	19,675	17,275	14,631	12,899	11,530	10,341	9,237	8,148	6,989	6,336	5,578	4,575	3,053	1,834
12	32,909	28,300	26,217	24,054	21,026	18,549	15,812	14,011	12,584	11,340	10,182	9,034	7,807	7,114	6,304	5,226	3,571	2,214
13	34,528	29,819	27,688	25,472	22,362	19,812	16,985	15,119	13,636	12,340	11,129	9,926	8,634	7,901	7,042	5,892	4,107	2,617
14	36,123	31,319	29,141	26,873	23,685	21,064	18,151	16,222	14,685	13,339	12,078	10,821	9,467	8,696	7,790	6,571	4,660	3,041
15	37,697	32,801	30,578	28,259	24,996	22,307	19,311	17,322	15,733	14,339	13,030	11,721	10,307	9,499	8,547	7,261	5,229	3,483
16	39,252	34,267	32,000	29,633	26,296	23,542	20,465	18,418	16,780	15,338	13,983	12,624	11,152	10,309	9,312	7,962	5,812	3,942
17	40,790	35,718	33,409	30,995	27,587	24,769	21,615	19,511	17,824	16,338	14,937	13,531	12,002	11,125	10,085	8,672	6,408	4,416
18	42,312	37,156	34,805	32,346	28,869	25,989	22,760	20,601	18,868	17,338	15,893	14,440	12,857	11,946	10,865	9,390	7,015	4,905
19	43,820	38,582	36,191	33,687	30,144	27,204	23,900	21,689	19,910	18,338	16,850	15,352	13,716	12,773	11,651	10,117	7,633	5,407
20	45,315	39,997	37,566	35,020	31,410	28,412	25,038	22,775	20,951	19,337	17,809	16,266	14,578	13,604	12,443	10,851	8,260	5,921
21	46,797	41,401	38,932	36,343	32,671	29,615	26,171	23,858	21,991	20,337	18,768	17,182	15,445	14,439	13,240	11,591	8,897	6,447
22	48,268	42,796	40,289	37,659	33,924	30,813	27,301	24,939	23,031	21,337	19,729	18,101	16,314	15,279	14,041	12,338	9,542	6,983
23	49,728	44,181	41,638	38,968	35,172	32,007	28,429	26,018	24,069	22,337	20,690	19,021	17,187	16,122	14,848	13,091	10,196	7,529
24	51,179	45,559	42,980	40,270	36,415	33,196	29,553	27,096	25,106	23,337	21,652	19,943	18,062	16,969	15,659	13,848	10,856	8,085
25	52,620	46,928	44,314	41,566	37,652	34,382	30,675	28,172	26,143	24,337	22,616	20,867	18,940	17,818	16,473	14,611	11,524	8,649
26	54,052	48,290	45,642	42,856	38,885	35,563	31,795	29,246	27,179	25,336	23,579	21,792	19,820	18,671	17,292	15,379	12,198	9,222

ν \ α	0,001	0,005	0,01	0,02	0,05	0,10	0,20	0,30	0,40	0,50	0,60	0,70	0,80	0,85	0,90	0,95	0,99	0,999
27	55,476	49,645	46,963	44,140	40,113	36,741	32,912	30,319	28,214	26,336	24,544	22,719	20,703	19,527	18,114	16,151	12,879	9,803
28	56,892	50,993	48,278	45,419	41,337	37,916	34,027	31,391	29,249	27,336	25,509	23,647	21,588	20,386	18,939	16,928	13,565	10,391
29	58,301	52,336	49,588	46,693	42,557	39,087	35,139	32,461	30,283	28,336	26,475	24,577	22,475	21,247	19,768	17,708	14,256	10,986
30	59,703	53,672	50,892	47,962	43,773	40,256	36,250	33,530	31,316	29,336	27,442	25,508	23,364	22,110	20,599	18,493	14,953	11,588
31	61,098	55,003	52,191	49,226	44,985	41,422	37,359	34,598	32,349	30,336	28,409	26,440	24,255	22,976	21,434	19,281	15,655	12,196
32	62,487	56,328	53,486	50,487	46,194	42,585	38,466	35,665	33,381	31,336	29,376	27,373	25,148	23,844	22,271	20,072	16,362	12,811
33	63,870	57,648	54,776	51,743	47,400	43,745	39,572	36,731	34,413	32,336	30,344	28,307	26,042	24,714	23,110	20,867	17,074	13,431
34	65,247	58,964	56,061	52,995	48,602	44,903	40,676	37,795	35,444	33,336	31,313	29,242	26,938	25,586	23,952	21,664	17,789	14,057
35	66,619	60,275	57,342	54,244	49,802	46,059	41,778	38,859	36,475	34,336	32,282	30,178	27,836	26,460	24,797	22,465	18,509	14,688
36	67,985	61,581	58,619	55,489	50,998	47,212	42,879	39,922	37,505	35,336	33,252	31,115	28,735	27,336	25,643	23,269	19,233	15,324
38	70,703	64,181	61,162	57,969	53,384	49,513	45,076	42,045	39,564	37,335	35,192	32,992	30,537	29,093	27,343	24,884	20,691	16,611
40	73,402	66,766	63,691	60,436	55,758	51,805	47,269	44,165	41,622	39,335	37,134	34,872	32,345	30,856	29,051	26,509	22,164	17,916
42	76,084	69,336	66,206	62,892	58,124	54,090	49,456	46,282	43,679	41,335	39,077	36,755	34,157	32,626	30,765	28,144	23,650	19,239
44	78,750	71,893	68,710	65,337	60,481	56,369	51,639	48,396	45,734	43,335	41,022	38,641	35,974	34,400	32,487	29,787	25,148	20,576
46	81,400	74,437	71,201	67,771	62,830	58,641	53,818	50,507	47,787	45,335	42,968	40,529	37,795	36,180	34,215	31,439	26,657	21,929
48	84,037	76,969	73,683	70,197	65,171	60,907	55,993	52,616	49,840	47,335	44,915	42,420	39,621	37,965	35,949	33,098	28,177	23,295
50	86,661	79,490	76,154	72,613	67,505	63,167	58,164	54,723	51,892	49,335	46,864	44,313	41,449	39,754	37,689	34,764	29,707	24,674
52	89,272	82,001	78,616	75,021	69,832	65,422	60,332	56,827	53,942	51,335	48,813	46,209	43,281	41,547	39,433	36,437	31,246	26,065
54	91,872	84,502	81,069	77,422	72,153	67,673	62,496	58,930	55,992	53,335	50,764	48,106	45,117	43,345	41,183	38,116	32,793	27,468
56	94,461	86,994	83,513	79,815	74,468	69,919	64,658	61,031	58,040	55,335	52,715	50,005	46,955	45,146	42,937	39,801	34,350	28,881
58	97,039	89,477	85,950	82,201	76,778	72,160	66,816	63,129	60,088	57,335	54,667	51,906	48,797	46,951	44,696	41,492	35,913	30,305
60	99,607	91,952	88,379	84,580	79,082	74,397	68,972	65,227	62,135	59,335	56,620	53,809	50,641	48,759	46,459	43,188	37,485	31,738
65	105,988	98,105	94,422	90,501	84,821	79,973	74,351	70,462	67,249	64,335	61,506	58,573	55,262	53,293	50,883	47,450	41,444	35,362
70	112,317	104,215	100,425	96,388	90,531	85,527	79,715	75,689	72,358	69,334	66,396	63,346	59,898	57,844	55,329	51,739	45,442	39,036
75	118,599	110,286	106,393	102,243	96,217	91,061	85,066	80,908	77,464	74,334	71,290	68,127	64,547	62,412	59,795	56,054	49,475	42,757
80	124,839	116,321	112,329	108,069	101,879	96,578	90,405	86,120	82,566	79,334	76,188	72,915	69,207	66,994	64,278	60,391	53,540	46,520
85	131,041	122,325	118,236	113,871	107,522	102,079	95,734	91,325	87,665	84,334	81,089	77,710	73,878	71,589	68,777	64,749	57,634	50,320
90	137,208	128,299	124,116	119,648	113,145	107,565	101,054	96,524	92,761	89,334	85,993	82,511	78,558	76,195	73,291	69,126	61,754	54,155
95	143,344	134,247	129,973	125,405	118,752	113,038	106,364	101,717	97,855	94,334	90,899	87,317	83,248	80,813	77,818	73,520	65,898	58,022
100	149,449	140,169	135,807	131,142	124,342	118,498	111,667	106,906	102,946	99,334	95,808	92,129	87,945	85,441	82,358	77,929	70,065	61,918