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Российская академия народного хозяйства и государственной службы при Президенте Российской Федерации

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ApPENDIX 'A:

AREAS UNDER THE NORMAL CURVE

Most of the examples in this book have used one version of the z-table ro find the area under the normal curve. This table provides the cumulative probabilities (or the area under the entire curve ro left of the z-value).

Probability Example

Assume that the annual earnings per share (EPS) for a large sample of firms is normally distributed with a mean of $5.00 and a standard deviation of $1.50. What is the approximate probability of an observed EPS value falling between $3.00 and $7.25?

If EPS = x = $7.25,	then z = (x - fL)la = ($7.25	-	$5.00)/$1.50 = + 1.50
If EPS = x = $3.00,	then z = (x- p.)la = ($3.00	-	55.(0)/51. SO = -1.33

Solving Using The Cumulative Z- Table

For z-Vfllue of1.50: Use the row headed 1.5 and the column headed 0 to find the value 0.9332. This represents the area under the curve to the left of the critical value 1.50.

For z-value (1-1.33: Use the row headed 1.3 and the column headed 3 to find the value 0.9082. This represents the area under the curve to the left of the critical value + 1.33. The area ro the left of -1.33 is 1 - 0.9082 = 0.0918.

The area between these critical values is 0.9332 - 0.0918 = 0.8414, or 84.14%.

Hypothesis Testing - One-Tailed Test Example

A sample of a srock's returns on 36 non-consecutive days results in a mean return of 2.0 percent. Assume the population standard deviation is 20.0 percent. Can we say with 95 percent confidence that the mean return is greater than zero percent?

H o: fL ::; 0.0%, Ha : p. > 0.0%. The test statistic = z-statistic = x -I~ = (2.0 - 0.0) 1

(20.0/6) =0.60. IT 1"n

The significance level = 1.0 - 0.95 = 0.05, or 5%. Since we are interested in a return greater than 0.0 percent, this is a one-tailed test.

Using The Cumulative Z-Table

Since this is a one-tailed test with an alpha of 0.05, we need to find the value 0.95 in the cumulative z-table. The closest value is 0.9505, with a corresponding critical z-value of 1.65. Since the test statistic is less than the critical value, we fail ro reject HO'

Page 351

Hypothesis Testing - Two-Tailed Test Example

Using the same assumptions as before, suppose that the analyst now wants ro determine ifhe can say with 99% confidence that the srock's rerum is not equal to 0.0 percent.

H o: 11 = 0.0%, H a: 11::;>t 0.0%.	The test statistic (z-value) = (2.0 - 0.0) / (20.0/6) = 0.60.
The significance level = 1.0 -	0.99 = 0.0 I, or 1%. Since we are interested in whether or

not the srock return is nonzero, this is a two-tailed test.

Using The Cumulative Z-Table

Since this is a two-tailed test with an alpha of 0.0 I, there is a 0.005 rejection region in both tails. Thus, we need to find the value 0.995 (1.0 - 0.005) in the table. The closest value is 0.9951, which corresponds to a critical z-value of 2. 58. Since the test statistic is less than the critical value. we fail to reject H o and conclude that the stock's rerum equals 0.0 percent.

Page 352

CUMULATIVE Z-TABLE

	STANDARD NORMAL DISTRIBUTION
	P(Z:S; z) = N(z) FOR Z 2:					0

		z	0.00		0.01		0.02		0.03	0.04		0.05		0.06	0.07	0.08	0.09
		0.0	0.5000		0.5040		0.5080		0.5120	0.5160		0.5199		0.5239	0.5279	0.5319	0.5359
		0.1	0.5398		0.5438		0.5478		0.5517	0.5557		0.5596		0.5636	0.5675	0.5714	0.5753
		0.2	0.5793		0.5832		0.5871		0.5910	0.5948		0.5987		0.6026	0.6064	0.6103	0.6141
		0.3	0.6179		0.6217		0.6255		0.6293	0.6331		0.6368		0.6406	0.6443	0.6480	0.6517
		0.4	0.6554		0.6591		0.6628		0.6664	0.6700		0.6736		0.6772	0.6808	0.6844	0.6879

		0.5	0.691')		0.<1')')0		O.69H,)		0.7019	0.7054		0. 7 088		0. 7 12.'\	0."'1 ')7	0.7190	0.7224	I
		0.6	0.7257	i	0.""2<) I		0."".::;24	I	0. 7 .:'>")7	0.7389		0.-422		0.:4')4	0.7486	0.7517	0.7')49
I		0.7	0.7580	,	0. 7 61 1		0.7642	i	0.7673	0.7704	I	0.--.1'-1		0.7 7 (14	O. ""7'>4 i	0.:823	0.7852
I		0.7	0.7580	i	0. 7 61 1		0.7642	i	0.7673	0.7704		0.--.1'-1		0.7 7 (14	O. ""7'>4 i	0.:823	0.7852
		0.8	0.7881		0.7910		0.7 9.19		0.7967	0.7995		0.8023		0.80')1	0.HO:8	0.8106	0.8133	I
		0.8	0.7881		0.7910		0.7 9.19	I	0.7967	0.7995		0.8023		0.80')1	0.HO:8	0.8106	0.8133
		0.9	0.8159		0.8186		0.8212		0.8238	0.8264		0.828')		0.83 J 'i	0.8340	0.8365	0.8389

		1.0	0.8413	!	0.8438		0.8461		0.8485	0.8508		0.85:'> 1	,	0.85')4	0.8'):7	0.8599	0.8621
		1.1	0.8643		0.8665		0.8686		0.8708	0.8729		0.8749		0.8770	0.8790	0.8810	0.88:'>0	i
		1.1	0.8643		0.8665		0.8686	i	0.8708	0.8729		0.8749		0.8770	0.8790	0.8810	0.88:'>0	!
		1.2	0.8849		0.8869		0.8888		0.8907	0.8925		0.8944		0.8962	0.8980	0.8997	0.9015
		1.3	0.9032		0.9049		0.9066		0.9082	0.9099		0.9115		0.913 ]	0.9]47	0.9162	0.9177	I
		1.4	0.9192		0.9207		0.9222		0.9236	0.9251		0.9265		0.9279	0.9292	0.9306	0.9'). I9. I,

		1.5	0.9332		0.9345		0.9357		0.9370	0.9382		0.9394		0.9406	0.9418	0.9429	0.9441
		1.6	0.9452		0.9463		0.9474		0.9484	0.9495		0.9505		0.9515	0.9525	0.9535	0.9545
		1.7	0.9554		0.9564		0.9573		0.9582	0.9591		0.9599		0.9608	0.9616	0.9625	0.9633
		1.8	0.9641		0.9649		0.9656		0.9664	0.9671		0.9678		0.9686	0.9693	0.9699	0.9706
		1.9	0.9713		0.9719		0.9726		0.9732	0.9738		0.9744		0.9750	0.9756	0.9761	0.9767

		2.0	0.9772		0.9778		0.9783		0.9788	0.9793		0.9798		0.9803	0.9808	0.9812	0.9817
		2.1	0.9821		0.9826		0.9830		0.9834	0.9838		0.9842		0.9846	0.9850	0.9854	0.9857
		2.2	0.9861		0.9864		0.9868		0.9871	0.9875		0.9878		0.9881	0.9884	0.9887	0.9890
		2.3	0.9893		0.9896		0.9898		0.9901	0.9904		0.9906		0.9909	0.9911	0.9913	0.9916
		2.4	0.9918		0.9920		0.9922		0.9925	0.9927		0.9929		0.9931	0.9932	0.9934	0.9936

I		2.5	0.9938		0.9940		0.9941		0.9943	0.9945		0.9946		0.9948	0.9949	0.9951	0.9952
		2.6	0.9953		0.9955		0.9956		0.9957	0.9959		0.9960		0.9961	0.9962	0.9963	0.9964
		2.7	0.9965		0.9966		0.9967		0.9968	0.9969		0.9970		0.9971	0.9972	0.9973	0.9974
		2.8	0.9974		0.9975		0.9976		0.9977	0.9977		0.9978		0.9979	0.9979	0.9980	0.9981
		2.9	0.9981		0.9982		0.9982		0.9983	0.9984		0.9984		0.9985	0.9985	0.9986	0.9986
		3.0	0.9987		0.9987		0.9987		0.9988	0.9988		0.9989		0.9989	0.9989	0.9990	0.9990

Page 353

CUMULATIVE Z-TABLE (CONT.)										----z				~
STANDARD NORMAL DISTRIBUTION
P(Z::; z) = N(z) FOR Z ::; 0

	z	0.00	0.01	0.02		0.03	0.04	0.05		0.06		0.07	0.08		0.09
	0.0	0.5000	0.4960	0.4920		0.4880	0.4840	0.4801		0.4761		0.4721	0.4681		004641
	-0. I	0.4602	004562	0.4522		0.4483	0.4443	0.4404		0.4364		0.4325	0.4286		004247
	-0.2	0.4207	0.4168	004129		0.4090	0.4052	004013		0.3974		0.3936	0.3897		0.3859
	-0.3	0.3821	0.3783	0.3745		0.3707	0.3669	0.3632		0.3594		0.3557	0.3520		0.3483
	-0.4	0.3446	0.3409	0.3372		0.3336	0.3300	0.3264		0.3228		0.3192	0.3] 56		0.3121

	-0.5	0.3085	0.30)0	0.3015		0.2981	0.2946	0.2912		0.2877		0.2843	0.2810		0.2776	)
I	-0.6	0.2743	0.2709 I	0.2(,76		lJ.')643	0.2611	0.2578		0.2546	I 0.2514		0.2483		0.2451
I	-0.7	0.2420	0.2389	0.23)1'	I	().232~	0.2297	0.2 / 66	I	0.2236	I	0.220-	0.2177		0.2148
I	-0.7	0.2420	0.2389	0.23)1'	I	().232~	0.2297	0.2 / 66	I	0.2236		0.220-	0.2177		0.2148
!	-0.8	0.2119	0.2090	0.206]	I	0.2033	0.2005	0.1977		0.1949		0.1922	0.1894		0.1867
i	-0.9	0.184]	0.] 814	0.1788		0.1762	0.1736	O.llll		0.1685		0.1660	0.1635		0.1611

	-1.0	0.1587	0.J562	0.1 'i39	I	0.1515	0.1492	0.1469		0.1446		0.1423	0.1401		0.1379
I	- J.]	0.1357	0.13.35	0.],)14	I	0.1292	I 0.]271	0.1251	,	0.1230		0.12] 0	0.1190		0.1] 70
	-1.2	0.115 I	0.1131	0.1112	i	0.1093	0.1075	O. I 057		O. ] 038		0.1020	0.1003		0.0985
	-1.3	0.0968	0.0951	0.0934		0.0918	0u90 I	0.0885		0.0869		0.0853	0.0838		0.0823
	-1.4	0.0808	0.0793	0.0778		0.0764	0.0749	0.0735		0.07 / 1		0.0708	0.0694		0.0681

	-1.5	0.0668	0.0655	0.0643	I	0.0630	0.0618	0.0606		0.0594		0.0582	0.0571		0.0559
	-1.6	0.0548	0.0537	0.0526		0.0516	0.0505	0.0495		0.0485		0.0475	0.0465		0.0455
	-1.7	0.0446	0.0436	0.0427		0.0418	0.0409	0.0401		0.0392		0.0384	0.0375		0.0367
	-1.8	0.0359	0.0351	0.0344		0.0336	0.0329	0.0322		0.0314		0.0307	0.0301		0.0294
	-1.9	0.0287	0.0281	0.0274		0.0268	0.0262	0.0256		0.0250		0.0244	0.0239		0.0233

	-2.0	0.0228	0.0222	0.0217		0.0212	0.0207	0.0202		0.0197		0.0192	0.0188		0.0183
	-2.1	0.0179	0.0174	0.0170		0.0166	0.0162	0.0158		0.0 154		0.0150	0.0146		0.0143
	-2.2	0.0139	0.0136	0.0132		0.0129	0.0125	0.0122		0.0119		0.0116	0.0113		0.0110
	-2.3	0.0107	0.0104	0.0]02		0.0099	0.0096	0.0094		0.0091		0.0089	0.0087		0.0084
	-2.4	0.0082	0.0080	0.0078		0.0076	0.0073	0.0071		0.0069		0.0068	0.0066		0.0064

	-2.5	0.0062	0.0060	0.0059		0.0057	0.0055	0.0054		0.0052		0.0051	0.0049		0.0048
	-2.6	0.0047	0.0045	0.0044		0.0043	0.0041	0.0040		0.0039		0.0038	0.0037		0.0036
	-2.7	0.0035	0.0034	0.0033		0.0032	0.0031	0.0030		0.0029		0.0028	0.0027		0.0026
	-2.8	0.0026	0.0025	0.0024		0.0023	0.0023	0.0022		0.0021		0.0021	0.0020		0.0019
	-2.9	0.0019	0.0018	0.0018		0.0017	0.0016	0.0016		0.0015		0.0015	0.0014		0.0014
	-3.0	0.0014	0.0013	0.0013		0.0012	0.0012	0.0011		0.0011		0.0011	0.0010		0.0010

Page 354

ApPENDIX B:

STUDENT'S T-DISTRIBUTION

										0.005

				Level of Significance for Two-Tailed Test
	df		0.20	0.10		0.05		0.02		0.01	0.001
	1		3.078	6.314		12.706		31.821		63.657	636.619
	2		1.886	2.920		4.303		6.965		9.925	31.599
	3		1.638	2.353		3.182		4.541		5.841	12.294
	4		1.533	2.132		2.776		3.747		4.604	8.610
	5		1.476	2.015		2.571		3.365		4.032	6.869
							I					,

I	6		1.440	1.945		2.44"-	!	5.1 if5	i	3.707	"i.')'i1J	j
	-		1.41 "i	1.895		2.3(1'i		2.9')S	I	3.499	"i A08	,
	8		1.397	1.860		2.3()(,	i	2.8%		3.355	'i.Oq I	I
	9		1.383	1.833		2.262		2.821		3.250	4.781
	10		1.372	1.812		2.228		2.764		3.169	4.58 7	I
							i
							I
	1 ]	I	1.363	1.7%		2.201		2.718		3.106	4.437
	1 ]	i	1.363	1.7%		2.201		2.718		3.106	4.437
	12	I	1.356	1.782		2.179		2.681		3.055	4.318
	13		1.350	1.771		2.160		2.650		3.012	4.221
	14		1.345	1.761		2.145		2.624		2.977	4.140
,	15		1..')41	1.753		2.131		2.602		2.947	4.073
i

	16		1.337	1.746		2.120		/.583		2.921	4.015
	17		1.333	1.740		2.110		2.567		2.898	3.965
	18		1.330	1.734		2.101		2.552		2.878	3.922
	19		1.328	1.729		2.093		2.539		2.861	3.883
	20		1.325	1.725	I	2.086		2.528		2.845	3.850
					I

					I

	21		1.323	1.721		2.080		2.518		2.831	3.819
	22		1.321	1.717		2.074		2.508		2.819	3.792
	23		1.319	1.714		2.069		2.500		2.807	3.768
	24		1.318	1.711		2.064		2.492		2.797	3.745
	25		1.316	1.708		2.060		2.485		2.787	3.725

	26		1.315	1.706		2.056		2.479		2.779	3.707
	27		1.314	1.703		2.052		2.473		2.771	3.690
	28		1.313	1.701		2.048		2.467		2.763	3.674
	29		1.311	1.699		2.045		2.q62		2.756	3.659
	30		1.310	1.697		2.042		2.457		2.750	3.646

	40		1.303	1.684		2.021		2.423		2.704	3.551
	60		1.296	1.671		2.000		2.390		2.660	3.460
	120		1.289	1.658		1.980		2.358		2.617	3.373
	00		1.282	1.645		1.960		2.326		2.576	3.291

Page 355

ApPENDIX C:

F-TABLE AT 5 PERCENT (UPPER TAIL)

F-TABLE, CRITICAL VALUES, 5 PERCENT IN UPPER TAIL

Degrees of freedom for the numerator along top row

Degrees of freedom for the denominator along side row

			1				2		3	4	5		6		7				8			9	10	12			IS		20		24		30			40
	1		161			200			216	2')-	230		234		237				239			241	242	244		246			248		249		250			251
	1		161			200			216	~)	230		234		237				239			241	242	244		246			248		249		250			251
	2		18.5			19.0			19.2	19.2	19.3		19.3		19.4				19.4			19.4	19.4	19.4		19.4			19.4		19.5		19.5			19.5
	3		10.1			9.55			9.28	9.12	9.01		8.94		8.89				8.85			8.81	8.79	8.74		8.70			8.66		8.64		8.62			8.59
	4		7.71			6.94			6.59	6.39	6.26		6.16		6.09				6.04			6.00	5.96	5.91		5.86			5.80		5.77		5.75			5.72
	5		6.61			5.79			5.41	5.19	5.05		4.95		4.88				4.82			4.77	4.74	4.68		4.62			4.56		4.53		4.50			4.46
																		I							I							I
I	6	i	'i.'ll)			'i.14			4. 7 (,	4. 'i5	4.19	I	'l.2fl	I	4.21			i	4.1 'i		I	4.10	I 4.06	4.00		?.94			3K7 i		3.84	i	un I			J -.~,
!	-		'i.'i')				7				.'1 'I-I		.,8-	!	5.	7	!)		~ - ,					-~	i					I			~)		!
!	-	I	'i.'i')		i	4.	7	4	4..1 'i	4.12	.'1 'I-I		.,8-	!	5.		!)		.J,	.'		3.68	3.64	3.~	i	3.'i1			3.4"1		3.'1l		~)	.:if>		'::U4
I		I	~.,1-		i	4.		4	4..1 'i	4.12									.J,	.'		3.68	3.64			3.'i1			3.4"1		3.'1l			.:if>		'::U4
i	8	i		_	!	11.46			4.07	3.84	:i. (,9		.ns i		3.'i0				3.44			3.39	335	3.2S		.'.--			3.1 'i i		3.12		3.08			3.04
i				_	!																						')"l
			')																							~
	') i 'i.]2					4.26			'::Ul6	3.63	3.4H		.)..')7		3.29				' )	~		3. I 8	3.14	3.07		6.01			2.94		2.90		2.86			2.83
	') i 'i.]2					4.26			'::Ul6	3.63	3.4H		.)..')7		3.29				J.~J			3. I 8	3.14	3.07		6.01			2.94		2.90		2.86			2.83
	10		4.%			4.10			3.71	3.48	3.31		3.22		3.14				3.07			3.02	2.98	2.91		2.85			2.77		2.74	I	2.70			2.66
		I									I																	I		\		i
I	1 1		4.84			.'1.98			3.59	3.36	.L!O		.3.09		3.01			I	2.9'i			2.90	').85	2.79		') .72		!	2.65		261 ! '.')7					'1 .. .,
I	1 1		4.84			.'1.98			3.59	3.36	.L!O	I	.3.09		3.01			I	2.9'i			2.90	').85	2.79		') .72		!	2.65		261 ! '.')7					_.) . )
I	12	I	4. 7 ')			.J.8')			I 3.49	3.26	3.; 1 i		3.00		2.91				2.8'i			2.80	2.75	2.69		2.62			2.54		2.51	i	2.47			2.43
I	1.3	I	4.67			5.8 I			3.41	3. I 8	3.cn		2.92		2.83			I	2.77			2.71	2.67	2.60		2.53		I	2.46		2.42		2.38			2.34
I	1.3	I	4.67			5.8 I			3.41	3. I 8	3.cn		2.92		2.83			I	2.77			2.71	2.67	2.60		2.53		I	2.46		2.42		2.38			2.34
	14		4.60			3.74			3.34	3.11	2.%	I	2.85		2.76				2.70			2.6'5	2.60	2.53		2.46			2.39		2.3'5	I	2.31			2.27
	15		4.54			).68			3.29	3.06	2.'>0	I	2. 7 9		2.71				2.64		I	2.59	254	2.48		2.40			2..'33		2.29	!	') ')-			2.20
	15		4.54			).68			3.29	3.06	2.'>0	I	2. 7 9		2.71				2.64		I	2.59	254	2.48		2.40			2..'33		2.29	!	_.~)			2.20
		I
	16		4.49			3.63			3.24	3.01	2.85		2.74		2.66				2.59			2.54	2.49	2.42		2.35			2.28		2.24		2.19			2.15
	17		4.45			3.59			3.20	2.96	2.81		2.70		2.61				2.55			2.49	2.45	2.38		2.31			2.23		2. I 9		2.15			2.10
	18		4.4]			3.55			3.16	2.93	2.77		2.66		2.58				2.5 I			2.46	2.41	2.34		2.27			2.19		2.15		2.1 I			2.0G
	19		4.38			3.52			3.13	2.90	2.74		2.G3		2.54				2.48			2.42	2.38	2.31		2.23			2.16		2.11		2.07			2.03
	20		4.35			3.49			3.10	2.87	2.71		2.60		2.')1				2.45			2.39	2.35	2.28		2.20			2.12		2.08		2.04			1.99

	21		4.32			3.47			3.07	2.84	2.G8		2.57		2.49				2.42			2.37	2.32	2.25		2.18			2.10		2.05		2.01			1.96
	22		4.30			3.44			3.05	2.82	2.66		2.55		2.46				2.40			2.34	2.30	2.23		2.15			2.07		2.03		1.98			1.94
	23		4.28			3.42			3.03	2.80	2.64		2.53		2.44				2.37			2.32	2.27	2.20		2.13			2.05		2.01		1.96			1.91
	24		4.26			3.40			3.0 I	2.78	2.62		2.51		2.42				2.%			2.30	2.25	2. I 8		2.1 I			2.03		1.98		1.94			1.89
	25		4.24			3.39			2.99	2.76	2.60		2.49		2.40				2.34			2.28	2.24	2.16		2.09			2.01		1.96		1.92			1.87

	30		4.17			.1.32			2.92	2.69	2.53		2.42		2.33				2.27			2.21	2.16	2.09		2.01			1.93		1.8')		1.84			1.79
	40		4.0B			3.23			2.84	2.61	2.45		2.34		2.25				2.18			2.12	2.08	2.00		1.92			1.84		1.79		J .74			1.69
	60		4.00			3.15			2.76	2.53	2.37		2.25		2. 17				2.10			2.04	1.99	1.92		1.84			1.75		1.70		1.65			1.59
	120		3.92			3.07			2.68	2.45	2.29		2.18		2.09				2.02			1.96	1.91	1.83		1.75			1.66		I.GI		1.55			1.50
	00		3.84			3.00			2.60	2.37	2.21		2.10		2.01				1.94			1.88	1.83	1.75		1.67			1.57		1.52		1.46			1.39

Page 356

ApPENDIX D:

F-TABLE AT 2.5 PERCENT (UPPER TAIL)

F-TABLE, CRITICAL VALUES, 2.5 PERCENT IN UPPER TAILS

Degrees of freedom for the numerator along top row

Degrees of freedom for the denominator along side row

	1	2				3	4	5		6	7		8		9		10	12	15	20		24	30		40
1	648	799				864	900		922	937	948		957		963		969	977	985	993		997	1001		1006
2	38.51	39.00				39.17	39.25		39.30	39.33	39.36		39.37		39.39		39.40	39.41	39.43	39.45		39.46	39.46		39.47
3	17.44	16.04				15.44	15.10		14.88	14.73	14.62		14.54		14.47		14.42	14.34	14.25	14.17		14.12	14.08		14.04
4	12.22	10.65				9.98	9.60		9.36	9.20	9.07		8.98		8.90		8.84	8.75	8.66	8.56		8.51	8.46		8.41
5	10.01	8.43				7.76	7.39	7.15		6.98	6.85		6.76		6.68		6.62	6.52	6.43	6.33		6.28	6.23		6.18	i
																										i
																										I
6	R.81	.., .2()				(,,60	6.23	5.99		5.82	').70		').60I		').')2		'iA()	'i.37	5.27	5.17		').12	'i.O-		').01
-	8.0-		(1. 'i4			').89	').52	, 5.29		5.12	4.<)9		4.90		:i.Rl	!	-'!.()'	4.67	4.')7	4.47		4.'t I	4 ..'\(,	,	't ..'1	I
,	'S-						I 5.05										11.30
,						5.42		4.82		4.65	't.55	I	4.4.1		4.36			4.20	4.10	4.00			.,.8')	I
8		(1.06		1								I									I	j.t)';			.'.H-'!
8		(1.06		1																	I				.'.H-'!


9	7.21	5.71			I	5.08	4. "',	4.48		4.32	4.20		4.10	!	4.03		.1.%	3.87	3.77	3.67		.'\.()1	.'\.')6		.1.') 1
9	7.21	5.71			I	5.08	4. "',	4.48		4.32	4.20		4.10		4.03		.1.%	3.87	3.77	3.67		.'\.()1	.'\.')6		.1.') 1
							' (~
10	6.94	5.46				4.83	4.47	4.24		4.07	3.95		3.85		3.78		3.72	3.62	3.52	3.42		3 ..r'	3.31		:'>.26
		I			I																			I		I
		I																						I		I

11	6.72	,	5.26			4.63	4.28		4.04	3.88	3.76		3.66		.1.')9		3.5.1	.1.43	3..)3	3.23		3.17	3.12		3.0()	,I
12	(,.55	5.10				4.47	I 4.12		3.89	3.73	.1.61	I .1.5\			3.44		:U7	3.28	3.18	3.07		.1.02	2.96		2.91	I
13	6.41	4.97				4.35	4.00		3.77	3.60	3.48		3.39		3.31	!	3.25	.1.15	3.05	2.95		2.80	2.84	I 2.78
14	6.30	4.86				4.24	3.89		3.66	3.50	3.38		3.29		3.21		3.15	.1.05	2.95	2.84		2. 7 9	2.73		2.67	I
15	6.20	4.77				4.15	3.80	3.58		3.41	3.29		3.20		3.12		3.06	2.96	2.86	2.76		2.70	2.64		2.59	!

16	6.12	4.69				4.08	3.73		3.50	3.34	3.22		3.12		3.05		2.99	2.89	2.79	2.68		2.63	2.57		2.51
17	6.04	4.62				4.01	3.66		3.44	3.28	3.16		3.06		2.98		2.92	2.82	2.72	2.62		2.56	2.50		2.44
18	5.98	4.56				3.95	3.61		3.38	3.22	3.10		3.01		2.93		2.87	2.77	2.67	2.56		2.50	2.44		2.38
19	5.92		4.51			3.90	3.56		3.33	3.17	3.05		2.96		2.88		2.82	2.72	2.62	2.51		2.45	2.39		2.33
20	5.87	4.46				3.86	3.51	3.29		3.13	3.0]		2.91		2.84		2.77	2.68	2.57	2.46		2.41	2.35		2.29

21	5.83	4.42				3.82	3.48	3.25		3.09	2.97		2.87		2.80		2.73	2.64	2.53	2.42		2..)7	2.31		2.25
22	5.79	4.38				3.78	3.44		3.22	3.05	2.93		2.84		2.76		2.70	2.60	2.50	2.39		2.33	') ..,...,		2.21
22	5.79	4.38				3.78	3.44		3.22	3.05	2.93		2.84		2.76		2.70	2.60	2.50	2.39		2.33	........ /		2.21
23	5.75	4.35				3.75	3.41		3.18	3.02	2.90		2.81		2.73		2.67	2.57	2.47	2.36		2.30	2.24		2.18
24	5.72	4.32				3.72	3.38		3.15	2.99	2.87		2.78		2.70		2.64	2.54	2.44	2.33		2.27	2.21		2.15
25	5.69	4.29				3.69	3.35	3.13		2.97	2.85		2.75		2.68		2.61	2.51	2.41	2.30		2.24	2.18		2.12

30	5.57	4.18				3.59	3.25	3.03		2.87	2.75		2.65		2.57		2.51	2.41	2.31	2.20		2.14	2.07		2.01
40	5.42	4.05				3.46	3.13		2.90	2.74	2.62		2.53		2.45		2.39	2.29	2.18	2.07		2.01	1.94		1.88
60	5.29	3.93				3.34	3.01	2.79		2.63	2.5J		2.41		2.33		2.27	2.17	2.06	1.94		l.RR	1.R2		1.74
120	5.15	3.80				3.23	2.89	2.67		2.52	2..19		2.30		2.22		2.16	2.05	1.94	1.82		1.76	1.69		1.61
00	5.02	3.69				3.12	2.79	2.57		2.41	2.29		2.19		2.11		2.05	1.94	1.83	1.71		1.64	1.57		1.48

Page 357

ApPENDIX E:

CHI-SQUARED TABLE

Values of X2 (Degrees of Freedom, Level of Significance)

Probability in Right Tail

Degrees of		0.99		0.975	0.95			0.9	0.1		0.05	0.025		0.01		0.005
Freedom		0.99		0.975	0.95			0.9	0.1		0.05	0.025		0.01		0.005
Freedom
1		0.000157		0.000982	0.003932			0.0158	2.706		3.841	5.024		6.635		7.879
2		0.020100		0.050636	0.102586			0.2107	4.605		5.991	7.378		9.210		10.597
3		0.1148		0.2158	0.3518			0.5844	6.251		7.815	9.348		11.345		12.838
4		0.297		0.484	0.711			1.064	7.779		9.488	11.143		13.277		14.860
5		0.554		0.831	1.145			1.610	9.236		11.070	12.832		15.086		16.750

6		OK'2		1.237	1.635			2.204	10.64')		12.592	14.449		16.8\2		18.')48	I
..,		1.239		1.690	2.16			2.833	1".01'		14.067	16.0Ll	,	] 8.4-:'')	I	20."78	!
,		1.239		1.690	2.16			2.833	1".01'		14.067	16.0Ll		] 8.4-:'')	I	20."78	I
		J .6,j7	I		')	...	I	3.·it)() I		i	1').50'					21.9')')	,
					')	,~~	I
8				2.180	_	1."			13.362			17.535	i	20.090	I
9	I	2.08~	i	2.700	3.32')			4.168	l4.684	I	16.919	]9.023		21.666	i	23.589	I
9	I	2.08~	i	2.700	3.32')			4.168	l4.684		16.919	]9.023		21.666		23.589	I
]0	I	2.558	I	3.247	3.940			4.8(,)	15.987		18.307	20.483		23.209		15.188
]0	I	2.558		3.247	3.940			4.8(,)	15.987		18.307	20.483		23.209		15.188

11		3.053		3.816	4.5 7 ')			';.578	17.275		19.675	21.920		24.725		26.7';7	i
12		3.571	I	4.404	5.226			6.304	18.549		21.026	23.337		1(,,217		28.300	I
12		3.571		4.404	5.226			6.304	18.549		21.026	23.337		1(,,217		28.300	I
13		4.10;	i	5.009	5.892			7.041	J9.812		22.362	24.736		27 .6S8	I	29.819	I
13		4.10;	i	5.009	5.892			7.041	J9.812		22.362	24.736		27 .6S8	I	29.819	I
14		4.66,)		5.629	6.571			7.790	21.064		23.685	26.119		29.141	I	31.319	I
															I
			!														I
IS		5.229		6.262	7.261			8.547	22.307		24.996	27.488		30.578		32.80]	I
IS		5.229		6.262	7.261			8.547	22.307		24.996	27.488		30.578		32.80]	I

16		5.812		6.908	7.962			9.312	23.542		26.296	28.845		32.000		.14.267
17		6.40H		7.564	8.672			10.085	24.769		27.587	30.191		33.409		35.718
18		7.015		8.231	9.390			10.865	25.989		28.869	31.526		34.805		37.156
19		7.633		8.907	10.117			11.651	27.204		30.144	32.852		36.191		38.582
20		8.260		9.591	10.851			12.443	28.412		31.410	34.170		37.566		39.997

21		8.897		10.283	11.591			13.240	29.615		32.671	35.479		38.932		41.401
22		9.542		10.982	12.338			14.041	30.813		33.924	36.781		40.289		42.796
23		10.]<)6		11.689	]3.091			14.848	32.007		35.172	38.076		41.638		44.18]
24		10.856		12.401	13.848			15.659	33.196		36.415	39.364		42.980		45.558
25		11. 524		13.120	14.611			16.473	34.382		37.652	40.646		44.314		46.928

26		12.198		13.844	15.379			17.292	35.563		38.885	41.923		45.642		48.290
27		12.878		14.573	16.1') 1			18.114	36.741		40.113	43.195		46.963		49.645
28		13.56')		15.308	16.928			18.939	37.916		41.337	44.461		48.278		50.994
29		14.256		16.047	17.708			19.768	39.087		42.557	45.722		49.588		52.335
30		14.953		16.791	18.493			20.599	40.256		43.773	46.979		50.892		53.672

50		29.707		32.357	34.764			3/.689	63.167		67.505	71.420		76.154		79.490
60		37.485		40.482	43.188			46.459	74.397		79.082	83.298		88.379		91.952
80		53.540		57.153	60.391			64.278	96.578		101.879	106.629		112.329		116.321
100		70.065		74.222	77.929			82.358	] 18.498		124.342	129.561		135.807		140.170

>age 358

INDEX -

absolute frequency 157

additional compensation arrangements 47 addition rule for probabilities 194 additivity principle 123

advance-decline line 334 alternative hypothesis 291 amortization 114 annuities 102

annuities due 102

a priori probability 192 arithmetic means 162

continuous random variable 233 continuous uniform distribution 241 contrarian view 332

correlation 204, 244 cost of capital 101 counting problems 214

Country Version of GIPS (CVG) 73 covariance 202

covariance given a joint probability function 207

cross-sectional data 269 cumulative absolute frequency 159

cumulative distrihution function 23'5 cumulative rebrivc frequency 1';9

bank discount yield (BUY)

1'1.2

Bayes' formula .211

data mining

.279

Bernoulli random variable

237

debit balances in brokerage accounts

334

biased estimator

170

decile 166

bimodal data set

164

decision rule

292, 296

binomial distribution

2.r

default risk premium 98

binomial formula

215

degrees of freedom

2"73

binomial random variable

237, 238

descriptive statistics

155

binomial tree 239

desirable properties of an estimator

272

bond-equivalent yield (BEY)

146

diligence and reasonable basis

disclosure of conflicts 57

discount factor

101

cash flow additivity principle

123

discounting

96,

101

cash position of mutual funds

332

discount rate

97, 101. 119

CD equivalent yield

144

discrete distribution

234

central limit theorem

269

discretely compounded returns

252

Chebyshev's inequality

171

discrete random variable 233

chi-square distribution

312

discrete uniform random variable 236

Code of Ethics 13

dispersion 168

coefficient of variation

172

distribution function 235

combination form ula

215

down transition probability

239

communication with clients 53

composites 70, 74

compounding frequency 112

effective annual rate (EAR)

compound interest 95,96

effective annual yield (EAY)

143

conditional expected values

201

efficient estimator 273

conditional probability

J 93

efficient market hypothesis (EMH)

330

conduct as members and candidates 65

empirical probability 192

confidence index

334

equality of population means 305

confidence interval 244, 272

equaliry of variances

31 5

confidence interval for the population mean

275

event 191

consistent estimator 273

excess kurtosis 176

continuous compounding

252

excess return

173

continuous distribution

234

exhaustive events 191

Page 359

Book 1 - Ethical and Professional Standards and Quantitative Methods

Index

expected value 198

cxpected value and variance for a portfolio of

aSSetS 206

of a binomial random variable 238

factorial 214 fair dealing 35

F-distriburion 316 frequency distribution 156 frequency polygon 160 fundamental analysts 330 future value (FY) 95

of an annuity due 105

of an ordinary annuity 102

of an uneven cash flow series 110 of ;\ single sum 100

gc'omelfiC mcall 1(''i ell'S objecrives -1

Global Investment Performance Standards

(GIPS) (,9

harmonic mean 166

histogram 160

histotical simulation 255

holding period rcrum (HPR) or holding period yield (HPY) 138,143

hypothesis 290

hypothesis tesring, steps 290

independence and ob;ectiviry		20
independent events	196
inferenrial statistics	155
inflation ptemium	98
inrerest on imerest	95
in tern a] rate of rerurn ORR)		] 35
IRR decision rule	136
IRR method 137

problems associated with 137 imerval 157

interval scale 156

investor credit balances in brokerage accounts 333

joint probability 193

knowledge of the law 17 kurtosis 175

interpretation 177

labeling 214

leprokurtic distributions 175 likelihood 193

liquidity risk premium 98 loan amortization 114

loan payment calculation 115

location of the mean, median, and mode 174

lognormal distribution 251 longitudinal data 269 look-ahead bias 280

lo\'alty, prudence. and care 33 loyalty (to emplover) 'f,)

marginal probability	193
market manipulation	31
material nonpublic information				28
malllrit)' risk premium 98
mean absolute deviation		168
mean differences 308
measuremenr scales	156
measures of central tendency			161
measurcs of location	167
median 163
mesokurtic distributions		175
misconduct 27
misrepresentation 24
modal inrerval 158
mode 164
money market yield	144
moncy-weighted rate of rcturn			138
Monte Carlo simulation		254
multiplication rule of probabiliry				193
multivariate distribution		243
multivariate normal disrribution				244
mutuallv cxclusive events		191

negative skew 174

net present value (NPY) 111, 133 NPY decision rule 136

node 239

nominal risk-free rate 98 nominal scales 156

non parametric tests 319 normal distribution 243 null hypothesis 291

Page 360

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