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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_155_библиотеки_им_акад_М_И_Перельмана
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Appendix B: Common Statistical Tables 369
Table B.10 (continued)
2 0.0046 0.0043 0.0040 0.0037 0.0034 0.0031 0.0029 0.0027 0.0025 0.0023
3 0.0140 0.0131 0.0123 0.0115 0.0107 0.0100 0.0093 0.0087 0.0081 0.0076
4 0.0319 0.0302 0.0285 0.0269 0.0254 0.0240 0.0226 0.0213 0.0201 0.0189
5 0.0581 0.0555 0.0530 0.0506 0.0483 0.0460 0.0439 0.0418 0.0398 0.0378
6 0.0881 0.0851 0.0822 0.0793 0.0764 0.0736 0.0709 0.0682 0.0656 0.0631
7 0.1145 0.1118 0.1091 0.1064 0.1037 0.1010 0.0982 0.0955 0.0928 0.0901
8 0.1302 0.1286 0.1269 0.1251 0.1232 0.1212 0.1191 0.1170 0.1148 0.1126
9 0.1317 0.1315 0.1311 0.1306 0.1300 0.1293 0.1284 0.1274 0.1263 0.1251
10 0.1198 0.1210 0.1219 0.1228 0.1235 0.1241 0.1245 0.1249 0.1250 0.1251
11 0.0991 0.1012 0.1031 0.1049 0.1067 0.1083 0.1098 0.1112 0.1125 0.1137
12 0.0752 0.0776 0.0799 0.0822 0.0844 0.0866 0.0888 0.0908 0.0928 0.0948
13 0.0526 0.0549 0.0572 0.0594 0.0617 0.0640 0.0662 0.0685 0.0707 0.0729
14 0.0342 0.0361 0.0380 0.0399 0.0419 0.0439 0.0459 0.0479 0.0500 0.0521
15 0.0208 0.0221 0.0235 0.0250 0.0265 0.0281 0.0297 0.0313 0.0330 0.0347
16 0.0118 0.0127 0.0137 0.0147 0.0157 0.0168 0.0180 0.0192 0.0204 0.0217
17 0.0063 0.0069 0.0075 0.0081 0.0088 0.0095 0.0103 0.0111 0.0119 0.0128
18 0.0032 0.0035 0.0039 0.0042 0.0046 0.0051 0.0055 0.0060 0.0065 0.0071
19 0.0015 0.0017 0.0019 0.0021 0.0023 0.0026 0.0028 0.0031 0.0034 0.0037
20 0.0007 0.0008 0.0009 0.0010 0.0011 0.0012 0.0014 0.0015 0.0017 0.0019
21 0.0003 0.0003 0.0004 0.0004 0.0005 0.0006 0.0006 0.0007 0.0008 0.0009
(continued)
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370 Appendix B: Common Statistical Tables
Table B.10 (continued)
22 0.0001 0.0001 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0004 0.0004
23 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002
24 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001
x λ
11 12 13 14 15 16 17 18 19 20
0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.0010 0.0004 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 0.0037 0.0018 0.0008 0.0004 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000
4 0.0102 0.0053 0.0027 0.0013 0.0006 0.0003 0.0001 0.0001 0.0000 0.0000
5 0.0224 0.0127 0.0070 0.0037 0.0019 0.0010 0.0005 0.0002 0.0001 0.0001
6 0.0411 0.0255 0.0152 0.0087 0.0048 0.0026 0.0014 0.0007 0.0004 0.0002
7 0.0646 0.0437 0.0281 0.0174 0.0104 0.0060 0.0034 0.0018 0.0010 0.0005
8 0.0888 0.0655 0.0457 0.0304 0.0194 0.0120 0.0072 0.0042 0.0024 0.0013
9 0.1085 0.0874 0.0661 0.0473 0.0324 0.0213 0.0135 0.0083 0.0050 0.0029
10 0.1194 0.1048 0.0859 0.0663 0.0486 0.0341 0.0230 0.0150 0.0095 0.0058
11 0.1194 0.1144 0.1015 0.0844 0.0663 0.0496 0.0355 0.0245 0.0164 0.0106
12 0.1094 0.1144 0.1099 0.0984 0.0829 0.0661 0.0504 0.0368 0.0259 0.0176
13 0.0926 0.1056 0.1099 0.1060 0.0956 0.0814 0.0658 0.0509 0.0378 0.0271
14 0.0728 0.0905 0.1021 0.1060 0.1024 0.0930 0.0800 0.0655 0.0514 0.0387
(continued)
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Appendix B: Common Statistical Tables 371
Table B.10 (continued)
15 0.0534 0.0724 0.0885 0.0989 0.1024 0.0992 0.0906 0.0786 0.0650 0.0516
16 0.0367 0.0543 0.0719 0.0866 0.0960 0.0992 0.0963 0.0884 0.0772 0.0646
17 0.0237 0.0383 0.0550 0.0713 0.0847 0.0934 0.0963 0.0936 0.0863 0.0760
18 0.0145 0.0256 0.0397 0.0554 0.0706 0.0830 0.0909 0.0936 0.0911 0.0844
19 0.0084 0.0161 0.0272 0.0409 0.0557 0.0699 0.0814 0.0887 0.0911 0.0888
20 0.0046 0.0097 0.0177 0.0286 0.0418 0.0559 0.0692 0.0798 0.0866 0.0888
21 0.0024 0.0055 0.0109 0.0191 0.0299 0.0426 0.0560 0.0684 0.0783 0.0846
22 0.0012 0.0030 0.0065 0.0121 0.0204 0.0310 0.0433 0.0560 0.0676 0.0769
23 0.0006 0.0016 0.0037 0.0074 0.0133 0.0216 0.0320 0.0438 0.0559 0.0669
24 0.0003 0.0008 0.0020 0.0043 0.0083 0.0144 0.0226 0.0328 0.0442 0.0557
25 0.0001 0.0004 0.0010 0.0024 0.0050 0.0092 0.0154 0.0237 0.0336 0.0446
26 0.0000 0.0002 0.0005 0.0013 0.0029 0.0057 0.0101 0.0164 0.0246 0.0343
27 0.0000 0.0001 0.0002 0.0007 0.0016 0.0034 0.0063 0.0109 0.0173 0.0254
28 0.0000 0.0000 0.0001 0.0003 0.0009 0.0019 0.0038 0.0070 0.0117 0.0181
29 0.0000 0.0000 0.0001 0.0002 0.0004 0.0011 0.0023 0.0044 0.0077 0.0125
30 0.0000 0.0000 0.0000 0.0001 0.0002 0.0006 0.0013 0.0026 0.0049 0.0083
31 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0007 0.0015 0.0030 0.0054
32 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0004 0.0009 0.0018 0.0034
33 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0005 0.0010 0.0020
34 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0006 0.0012
(continued)
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372 Appendix B: Common Statistical Tables
Table B.10 (continued)
35 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0007
36 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0004
37 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002
38 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001
39 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001
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Appendix B: Common Statistical Tables 373
Table B.11 Negative exponential distribution table
0 1 2 3 4 5 6 7
0 1 0.3679 0.1353 0.0498 0.0183 0.0067 0.0025 0.0009
0.1 0.9048 0.3329 0.1224 0.0450 0.0166 0.0061 0.0022 0.0008
0.2 0.8187 0.3012 0.1108 0.0408 0.0150 0.0055 0.0020 0.0007
0.3 0.7408 0.2725 0.1003 0.0369 0.0136 0.0050 0.0018 0.0007
0.4 0.6703 0.2466 0.0907 0.0334 0.0123 0.0045 0.0017 0.0006
0.5 0.6065 0.2231 0.0821 0.0302 0.0111 0.0041 0.0015 0.0006
0.6 0.5488 0.2019 0.0743 0.0273 0.0100 0.0037 0.0014 0.0005
0.7 0.4966 0.1827 0.0672 0.0247 0.0091 0.0033 0.0012 0.0005
0.8 0.4493 0.1653 0.0608 0.0224 0.0082 0.0030 0.0011 0.0004
0.9 0.4066 0.1496 0.0550 0.0202 0.0076 0.0027 0.0010 0.0004
Table B.12 Exponential distribution table: The exponential distribution is often concerned with
the amount of time until some specific event occurs
0 1 2 3 4 5 6 7
0 1.00 2.72 7.39 20.09 54.60 148.41 403.43 1096.63
0.1 1.11 3.00 8.17 22.20 60.34 164.02 445.86 1211.97
0.2 1.22 3.32 9.07 24.53 66.69 181.27 492.75 1339.43
0.3 1.35 3.67 9.97 27.11 73.70 200.34 544.57 1480.30
0.4 1.49 4.06 11.02 29.96 81.45 221.41 601.85 1635.98
0.5 1.65 4.48 12.18 33.12 90.02 244.69 665.14 1808.04
0.6 1.82 4.95 13.46 36.6 99.48 270.43 735.10 1998.20
0.7 2.01 5.47 14.88 40.45 109.95 298.87 812.41 2208.35
0.8 2.23 6.05 16.44 44.70 121.51 330.30 897.85 2440.60
0.9 2.46 6.69 18.17 49.4 134.29 365.04 992.27 2697.28
Table B.13 Required sample size to estimate a proportion (alpha = 0.05)
Margin of error P 0.05 0.1 0.2 0.25 0.33 0.5
0.50 1537 384 97 62 35 16
0.45 1879 470 118 76 43 19
0.40 2305 577 145 93 52 24
0.35 2855 714 179 115 65 29
0.30 3586 897 225 144 81 36
0.25 410 1153 289 185 104 47
0.20 6147 1537 385 246 139 62
(continued)
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374 Appendix B: Common Statistical Tables
Table B.13 (continued)
Margin of error P 0.05 0.1 0.2 0.25 0.33 0.5
0.15 8707 2177 545 349 196 88
0.10 13,830 3458 865 554 312 139
0.08 17,672 4418 1105 707 398 177
0.06 24,075 6019 1505 963 542 241
0.05 29,197 7299 1825 1168 657 292
0.03 49,685 12,422 3106 1988 1118 497
0.02 75,296 18,824 4706 3012 1695 753
0.01 152,128 38,032 9508 6086 3423 1522
0.008 190,544 47,636 11,909 7622 4288 1906
0.006 254,570 63,643 15,911 10,183 5728 2546
0.005 305,792 76,448 19,112 12,232 6881 3058
0.003 510,677 127,670 31,918 20,428 11,491 5107
0.002 766,784 191,696 47,924 30,672 17,253 7668
0.001 1,535,103 383,776 95,944 61,405 34,540 15,352
Table B.14 Required sample size to estimate a proportion (alpha = 0.05)
Margin of error P 0.05 0.10 0.20 0.25 0.33 0.50
0.50 1083 271 68 44 25 12
0.45 1324 331 83 54 31 14
0.40 1624 406 102 66 37 17
0.35 2011 503 126 81 46 21
0.30 2526 632 158 102 57 26
0.25 3248 812 203 131 74 34
0.20 4330 1083 271 174 98 44
0.15 6134 1534 384 246 139 62
0.10 9742 2436 609 391 220 98
0.08 12,449 3112 778 498 281 125
0.06 16,959 4240 1060 679 382 170
0.05 20,567 5142 1284 823 463 206
0.03 34,999 8750 2188 1400 788 351
(continued)
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Appendix B: Common Statistical Tables 375
Table B.14 (continued)
Margin of error P 0.05 0.10 0.20 0.25 0.33 0.50
0.02 53,039 13,260 3315 212 1194 531
0.01 107,160 26,790 6698 4287 2412 1073
0.008 134,220 33,555 8389 5369 3021 1343
0.006 179,320 44,830 11,208 7173 4035 1794
0.005 215,400 53,850 13,463 8617 4847 2155
0.003 359,721 89,931 22,483 14,390 8095 3598
0.002 540,123 135,031 33,758 21,606 12,154 5402
0.001 1,081,328 270,332 67,583 43,254 24,330 10,814
Table B.15 Square of sum of s
z
α
2
+ z
β
2
α 0/40 0/20 0/10 0/05 0/02 0/01 0/002 0/001 0/0001 0/00001
β Z 0.84 1.28 1.64 1.96 2.33 2.58 3.09 3.29 3.89 4.42
0.40 0.84 2.82 4.5 7.84 7/84 1/020 11.67 15.44 17.06 22.38 27.64
0.2 1.28 4.5 6.57 10.51 1/510 1/023 14.88 19.11 20.91 26.76 32.48
0.1 1.64 6.17 8.57 12.99 1/992 1/775 17.82 22.42 24.36 30.65 36.75
0.05 1.96 7.84 10.51 15.37 1/375 1/378 20.57 25.5 27.57 34.23 40.67
0.02 2.33 10.02 13,02 18.37 1/378 2/641 24.03 29.33 31.55 38.65 45.47
0.01 2.58 11.67 14.88 20.57 2/570 2/034 26.54 32.1 34.42 41.82 48.9
0.002 3.09 15.45 19.11 25.5 2/505 2/339 32.1 38.19 40.72 48.73 56.35
0.001 3.29 17.06 20.91 27.57 2/577 3/551 34.42 40.72 43.32 51.58 59.41
0.0001 3.89 22.38 26.76 34.23 3/234 3/658 41.82 48.73 51.58 60.56 69.02
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Answer to Exercises
In order to make sure that the reader and the student can complete the exercises and
questions at the end of each chapter, we offer the final answer (not the solution) in
this section, having chosen a portion of them at random.
Chapter 1
1-A Shoe sizes are both quantitative and interval; the difference between any two half sizes
is approximately 5 mm, and the zero has no meaning. The sizes of clothing (…, XS, S,
M, L, XL, and XXL, ….) is ordinal and qualitative in nature
1-E Quantitative and continuous
1-G Quantitative and interval
1-L Qualitative and nominal
1-N Quantitative and continuous
1-O Quantitative and discrete
1-S Qualitative and ordinal
1-T Quantitative and discrete
1-Z Quantitative and discrete
Chapter 2
Q2 Pie diagram
Q4 Bar and pie diagram
Q7 Finding the l owest and highest observations (X
min
= 0, X
max
= 12) as well as the three
quartiles (Q
1
= 3, Q
2
= median = 5, Q
3
= 8) is necessary in order to create a boxplot.
In this case, there isn’t an outlier
Chapter 3
Q3 Mean = 1.725, median = 2, Q
3
= 3, Var = 1.310, and SD = 1.145
Q5 Since the coefficient of variation takes into account both the population means and the
standard deviation, it is more appropriate
(continued)
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2024
S. H. Saneii and H. Doosti, Practical Biostatistics for Medical and Health Sciences,
https://doi.org/10.1007/978-981-97-3083-4
377
https://t.me/med1917
378 Answer to Exercises
(continued)
Chapter 1
Q8 Q
1
= 244.14, Q
3
= 328.96 and p70 = 317.67
Q10 Man = 4.1, median = 4.05, Var = 0.514, and Sd = 0.717
Chapter 4
Q3 p(x = 4) = 0.01234 and p(x = 0) = 0.1975
Q6 p = 68/200 = 0.32 and n = 7
A: one every other means that p(YNYNYNY or NYNYNYN) = 0.00329 + 0.007 =
0.1030
B: Only the first three patients means that p(YYYNNNN) = 0.007
C: 0.245
Q8 p(old) = 0.50
p(Young) = 0.50
p(H|O) = 0.35
p(H|Y ) = 0.15
P(OH) = 0.35 × 0.50 = 0.175,
P
Y
|
H
= 0.85 × 0.50 = 0.425,
P(H ) = (0.50 × 0.35) + (0.50 × 0.15) = 0.25
Q10 P
®
= 0.3333, P(Y ) = 0.6666
A: All three seedlings are red: P(X = 3R) = 0.037
B: Maximum of two yellow: P(X ≤ 2) = 0.704
C: At least one yellow:P(X ≥ 1) = 0.963
Q14 P(A) = 0.6
A: The match will be finished in three sets. p(X = ABA) + p(BAB) = 0.24
B: The match ends in two sets. p(X = AA) + p(X = BB) = 0.58
Q19 Since Step Down model and Step Up model are independent events, P(A*B) =
P(A)*P(B) = 0.05*0.03 = 0.0015 and the probability at least one of the model is:
P(A + B) = P(A or B) = 0.05 + 0.03–0.0015 = 0.0785
Q24 P(orbit) =
1
7
. n = 5
P(x ≥ 3) = p(X = 3) + P(x = 4) + p(x = 5) = 0.0647
Chapter 5
Q1 μ = λ =
1
4
and p(2) = 0.0042
Q3 P = 0.2 and n = 6
A: p(x = 2) = 0.246
B: p
(
x
≤ 2
)
= p
(
x = 0
)
+ p
(
x = 1
)
+ p
(
X = 2
)
= 0.9011
C: Maximum of 2 patients survive which means that minimum of 4 patients die
p
(
X
≥ 2
)
= 0.01696
D: p(X = 1) = 0.3932
Q5 μ = λ = 6000 ×
1
1000
= 6andp
(
x ≤ 2
)
= 0.062
Q7 p =
1
4
= 0.25, n = 10 and x = 6
Using binomial distribution: p(x = 6) = 0.01622
(continued)
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Answer to Exercises 379
(continued)
Chapter 1
Q8 μ = λ = 2000 × 0.002 = 4and p
(
x = 0
)
= 0.183
Q12 μ = λ = 10 and p
(
x = 0
)
= 0.000045
Chapter 6
Q4 X ∼ N (100, 15)
P(X > 126) = 1 − P(X ≤ 126) = 0.0418 or 4.18%
Q6 X ∼ N (120, 15)
C = 0.75 → P
(
−0.75 ≤
Z ≤+0.75
)
= 0.50
Q9 X ∼ N (600, 100)
P
(
650 ≤ X ≤
750
)
= 0.2417
Q11 X ∼ N (30, 5.5)
P
(
X ≥
20
)
= 0.9656
or 96.56%
Q14 Yes, because calculated χ
2
= 8.35 >χ
2
2
= 5.99
Chapter 7
Q3 n = 34
Q5 P = 0.4, d = 0.2 × 0.4 = 0.08, and n = 144
Q7 n = 385
Q10 P = 0.333 and 1−p = 0.666. Assuming 0.05 if significant level and the maximum
difference of 10% lead to n = 86
Chapter 8
Q2 P = 0.40, n = 225, and CI = 0.336–0.464
Q4 For n = 100:
A: z
0.975
= 1.96 and CI = 22.04–24.36
B: z
0.995
= 2.575 and CI = 21.68–24.72
C:For n = 20:
t
19 and 0.975
= 2.093 and CI = 20.44–25.96
t
19 and 0.995
= 2.539 and CI = 19.85–26.55
Q6 n = 64, Sd = 12, and mean = 105
95% confidence interval (102–108) includes the actual mean blood pressure of the
population
Q8 P =
11
80
= 0.1375, n = 30, t
29
= 2.045,thenCI = 0.0588–0.216
(continued)
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