tabel complete (z, t, binomial)
TRANSCRIPT
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7/28/2019 Tabel Complete (z, t, Binomial)
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7/28/2019 Tabel Complete (z, t, Binomial)
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Table 5 Areas of a Standard Normal Distribution
The table entries represent the area under the standardnormal curve from 0 to the specified value of z.
z
0.00.10.20.30.40.5
.00
.0000
.0398
.0793
.1179
.1554
.1915
.01
.0040
.0438
.0832
.1217
.1591
.1950
.02
.0080
.0478
.0871
.1255
.1628
.1985
.03
.0120
.0517
.0910
.1293
.1664
.2019
.04
.0160
.0557
.0948
.1331
.1700
.2054
.05
.0199
.0596
.0987
.1368
.1736
.2088
.06
.0239
.0636
.1026
.1406
.1772
.2123
.07
.0279
.0675
.1064
.1443
.1808
.2157
.08
.0319
.0714
.1103
.1480
.1844
.2190
.09
.0359
.0753
.1141
.1517
.1879
.2224
0.60.70.80.91.0
.2257
.2580
.2881
.3159
.3413
.2291
.2611
.2910
.3186
.3438
.2324
.2642
.2939
.3212
.3461
.2357
.2673
.2967
.3238
.3485
.2389
.2704
.2995
.3264
.3508
.2422
.2734
.3023
.3289
.3531
.2454
.2764
.3051
.3315
.3554
.2486
.2794
.3078
.3340
.3577
.2517
.2823
.3106
.3365
.3599
.2549
.2852
.3133
.3389
.3621
1.11.21.31.41.5
.3643
.3849
.4032
.4192
.4332
.3665
.3869
.4049
.4207
.4345
.3686
.3888
.4066
.4222
.4357
.3708
.3907
.4082
.4236
.4370
.3729
.3925
.4099
.4251
.4382
.3749
.3944
.4115
.4265
.4394
.3770
.3962
.4131
.4279
.4406
.3790
.3980
.4147
.4292
.4418
.3810
.3997
.4162
.4306
.4429
.3830
.4015
.4177
.4319
.4441
1.61.71.81.92.0
.4452
.4554
.4641
.4713
.4772
.4463
.4564
.4649
.4719
.4778
.4474
.4573
.4656
.4726
.4783
.4484
.4582
.4664
.4732
.4788
.4495
.4591
.4671
.4738
.4793
.4505
.4599
.4678
.4744
.4798
.4515
.4608
.4686
.4750
.4803
.4525
.4616
.4693
.4756
.4808
.4535
.4625
.4699
.4761
.4812
.4545
.4633
.4706
.4767
.4817
2.12.22.3
2.42.5
:4821.4861.4893
.4918
.4938
.4826
.4864
.4896
.4920
.4940
:4830.4868.4898
.4922
.4941
.4834
.4871
.4901
.4925
.4943
.4838
.4875
.4904
.4927
.4945
.4842
.4878
.4906
.4929
.4946
.4846
.4881
.4909
.4931
.4948
.4850
.4884
.4911
.4932
.4949
.4854
.4887
.4913
.4934
.4951
.4857
.4890
.4916
.4936
.4952
2.62.72.82.93.0
.4953
.4965
.4974
.4981
.4987
.4955
.4966
.4975
.4982
.4987
.4956
.4967
.4976
.4982
.4987
.4957
.4968
.4977
.4983
.4988
.4959
.4969
.4977
.4984
.4988
.4960
.4970
.4978
.4984
.4989
.4961
.4971
.4979
.4985
.4989
.4962
.4972
.4979
.4985
.4989
.4963
.4973
.4980
.4986
.4990
.4964
.4974
.4981
.4986
.4990
3.13.23.33.43.5
3.6
.4990
.4993
.4995
.4997
.4998
.4998
.4991
.4993
.4995
.4997
.4998
.4998
.4991
.4994
.4995
.4997
.4998
.4998
.4991
.4994
.4996
.4997
.4998
.4999
.4992
.4994
.4996
.4997
.4998
.4999
.4992
.4994
.4996
.4997
.4998
.4999
.4992
.4994
.4996
.4997
.4998
.4999
.4992
.4995
.4996
.4997
.4998
.4999
.4993
.4995
.4996
.4997
.4998
.4999
.4993
.4995
.4997
.4998
.4998
.4999
For values of z greater than or equal to 3.70, use 0.4999 to approximate the shaded area under the standard normal curve.
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Table 6 Students t Distribution
Students t values generated by Minitab Version 9.2c 0.750 0.800 0.850 0.900 0.950 0.980 0.9
a 0.125 0.100 0.075 0.050 0.025 0.010 0.0
a 0.250 0.200 0.150 0.100 0.050 0.020 0.0
d.f.
1 2.414 3.078 4.165 6.314 12.706 31.821 63.6
2 1.604 1.886 2.282 2.920 4.303 6.965 9.9
cis a confidence level: 3 1.423 1.638 1.924 2.353 3.182 4.541 5.8
4 1.344 1.533 1.778 2.132 2.776 3.747 4.6
5 1.301 1.476 1.699 2.015 2.571 3.365 4.0
6 1.273 1.440 1.650 1.943 2.447 3.143 3.7
7 1.254 1.415 1.617 1.895 2.365 2.998 3.4
8 1.240 1.397 1.592 1.860 2.306 2.896 3.3
9 1.230 1.383 1.574 1.833 2.262 2.821 3.2
10 1.221 1.372 1.559 1.812 2.228 2.764 3.1
11 1.214 1.363 1.548 1.796 2.201 2.718 3.1
12 1.209 1.356 1.538 1.782 2.179 2.681 3.0ais the level of significance for a one-tailed test: 13 1.204 1.350 1.530 1.771 2.160 2.650 3.0
14 1.200 1.345 1.523 1.761 2.145 2.624 2.9
15 1.197 1.341 1.517 1.753 2.131 2.602 2.9
16 1.194 1.337 1.512 1.746 2.120 2.583 2.9
17 1.191 1.333 1.508 1.740 2.110 2.567 2.8
18 1.189 1.330 1.504 1.734 2.101 2.552 2.8
19 1.187 1.328 1.500 1.729 2.093 2.539 2.8
20 1.185 1.325 1.497 1.725 2.086 2.528 2.8
21 1.183 1.323 1.494 1.721 2.080 2.518 2.8
22 1.182 1.321 1.492 1.717 2.074 2.508 2.8
23 1.180 1.319 1.489 1.714 2.069 2.500 2.8
24 1.179 1.318 1.487 1.711 2.064 2.492 2.7
25 1.178 1.316 1.485 1.708 2.060 2.485 2.7
26 1.177 1.315 1.483 1.706 2.056 2.479 2.7
27 1.176 1.314 1.482 1.703 2.052 2.473 2.7
28 1.175 1.313 1.480 1.701 2.048 2.467 2.7
29 1.174 1.311 1.479 1.699 2.045 2.462 2.7
a is the level of significance for a two-tailed test 30 1.173 1.310 1.477 1.697 2.042 2.457 2.7
35 1.170 1.306 1.472 1.690 2.030 2.438 2.7
40 1.167 1.303 1.468 1.684 2.021 2.423 2.7
45 1.165 1.301 1.465 1.679 2.014 2.412 2.6
50 1.164 1.299 1.462 1.676 2.009 2.403 2.6
55 1.163 1.297 1.460 1.673 2.004 2.396 2.6
60 1.162 1.296 1.458 1.671 2.000 2.390 2.6
90 1.158 1.291 1.452 1.662 1.987 2.369 2.6
120 1.156 1.289 1.449 1.658 1.980 2.358 2.6
cc 1.15 1.28 1.44 1.645 1.96 2.33 2.
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Areas of a Standard Normal Distribution
The table entries represent the area under the standard normal curve from 0 to thespecified value of z.
z
0.0
0.1
0.2
0.3
0.4
0.5
.00
.0000
.0398
.0793
.1179
.1554
.1915
.01
.0040
.0438
.0832
.1217
.1591
.1950
.02
.0080
.0478
.0871
.1255
.1628
.1985
.03
.0120
.0517
.0910
.1293
.1664
.2019
.04
.0160
.0557
.0948
.1331
.1700
.2054
.05
.0199
.0596
.0987
.1368
.1736
.2088
.06
.0239
.0636
.1026
.1406
.1772
.2123
.07
.0279
.0675
.1064
.1443
.1808
.2157
.08
.0319
.0714
.1103
.1480
.1844
.2190
.09
.0359
.0753
.1141
.1517
.1879
.2224
0.6
0.7
0.8
0.9
1.0
.2257
.2580
.2881
.3159
.3413
.2291
.2611
.2910
.3186
.3438
.2324
.2642
.2939
.3212
.3461
.2357
.2673
.2967
.3238
.3485
.2389
.2704
.2995
.3264
.3508
.2422
.2734
.3023
.3289
.3531
.2454
.2764
.3051
.3315
.3554
.2486
.2794
.3078
.3340
.3577
.2517
.2823
.3106
.3365
.3599
.2549
.2852
.3133
.3389
.3621
1.1
1.2
1.3
1.4
1.5
.3643
.3849
.4032
.4192
.4332
.3665
.3869
.4049
.4207
.4345
.3686
.3888
.4066
.4222
.4357
.3708
.3907
.4082
.4236
.4370
.3729
.3925
.4099
.4251
.4382
.3749
.3944
.4115
.4265
.4394
.3770
.3962
.4131
.4279
.4406
.3790
.3980
.4147
.4292
.4418
.3810
.3997
.4162
.4306
.4429
.3830
.4015
.4177
.4319
.4441
1.6
1.7
1.8
1.9
2.0
.4452
.4554
.4641
.4713
.4772
.4463
.4564
.4649
.4719
.4778
.4474
.4573
.4656
.4726
.4783
.4484
.4582
.4664
.4732
.4788
.4495
.4591
.4671
.4738
.4793
.4505
.4599
.4678
.4744
.4798
.4515
.4608
.4686
.4750
.4803
.4525
.4616
.4693
.4756
.4808
.4535
.4625
.4699
.4761
.4812
.4545
.4633
.4706
.4767
.4817
2.1
2.2
2.3
2.4
2.5
:4821
.4861
.4893
.4918
.4938
.4826
.4864
.4896
.4920
.4940
:4830
.4868
.4898
.4922
.4941
.4834
.4871
.4901
.4925
.4943
.4838
.4875
.4904
.4927
.4945
.4842
.4878
.4906
.4929
.4946
.4846
.4881
.4909
.4931
.4948
.4850
.4884
.4911
.4932
.4949
.4854
.4887
.4913
.4934
.4951
.4857
.4890
.4916
.4936
.4952
2.6
2.7
2.8
2.9
3.0
.4953
.4965
.4974
.4981
.4987
.4955
.4966
.4975
.4982
.4987
.4956
.4967
.4976
.4982
.4987
.4957
.4968
.4977
.4983
.4988
.4959
.4969
.4977
.4984
.4988
.4960
.4970
.4978
.4984
.4989
.4961
.4971
.4979
.4985
.4989
.4962
.4972
.4979
.4985
.4989
.4963
.4973
.4980
.4986
.4990
.4964
.4974
.4981
.4986
.4990
3.1
3.2
3.3
3.4
3.5
3.6
.4990
.4993
.4995
.4997
.4998
.4998
.4991
.4993
.4995
.4997
.4998
.4998
.4991
.4994
.4995
.4997
.4998
.4998
.4991
.4994
.4996
.4997
.4998
.4999
.4992
.4994
.4996
.4997
.4998
.4999
.4992
.4994
.4996
.4997
.4998
.4999
.4992
.4994
.4996
.4997
.4998
.4999
.4992
.4995
.4996
.4997
.4998
.4999
.4993
.4995
.4996
.4997
.4998
.4999
.4993
.4995
.4997
.4998
.4998
.4999For values of z greater than or equal to 3.70, use 0.4999 to approximate the shaded area under the standard normal curve.
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Some Levels of Confidence and Their Corresponding
Critical Values
Commonly Used Critical Values z0from the Standard
Normal Distribution
Level of Confidence c Critical Value zc Type of Test Level of Significance
0.75 1.15 0.05 0.01
0.80 1.28
0.85 1.44 Left-tailed - 1.645 -2.330.90 1.645 Right-tailed 1.645 2.330.95 1.96 Two-tailed 1.96 2.580.99 2.58
Table 8 Critical Values of Pearson Product-Moment Correlation Coefficient, r
a =0.01 a = 0.05
n one tail two tails one tail two tails
3 1.00 1.00 .99 1.00For a right-tailed test, use a positive rvalue: 4 .98 .99 .90 .95
5 .93 .96 .81 .886 .88 .92 .73 .81
7 .83 .87 .67 .758 .79 .83 .62 .719 .75 .80 .58 .67
10 .72 .76 .54 .6311 .69 .73 .52 .6012 .66 .71 .50 .58
For a left-tailed test, use a negative rvalue: 13 .63 .68 .48 .5314 .61 .66 .46 .5315 .59 .64 .44 .5116 .57 .62 .42 .5017 .56 .61 .41 .4818 .54 .59 .40 .4719 .53 .58 .39 .4620 .52 .56 .38 .4421 .50 .55 .37 .4322 .49 .54 .36 .42
For a two-tailed test, use a positive rvalue 23 .48 .53 .35 .41and negative r value: 24 .47 .52 .34 .40
25 .46 .51 .34 .4026 .45 .50 .33 .3927 .45 .49 .32 .3828 .44 .48 .32 .3729 .43 .47 .31 .3730 .42 .46 .31 .36
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Frequently Used Formulas
n = sample size N= population size f= frequency
Chapter 1
Class Width =classesofnumber
lowhigh (increase to next
integer)
Class Midpoint =2
lowerlimitupperlimit +
Lower boundary = lower boundary of previous class +class width
Chapter 2
Sample mean X=n
x
Population mean =N
x
Range = largest data value - smallest data value
Sample standard deviations s =1n
2)x(x
Computation formula s =1n
xSS
where
( )
=
n
2x2
xxSS
Population standard deviation( )
N
x =
2
Sample variance2s
Population variance2
o
Sample Coefficient of Variation 100=x
sCV
Sample mean for grouped datan
xfx
=
Sample standard deviation for grouped data
( )
1
2
=
n
fxxs
Chapter 3
Regression and Correlation
In all these formulas
( )
=
n
2x2
xxSS
( )
=
n
22
yySSy
( )( )
=
n
yxxyxySS
Least squares line bxay += wherexSS
xySSb = and
xbya =
Pearson product-moment correlation coefficient
ySSxSS
xySSr =
Coefficient of determination2
r=
Chapter 4
Probability of the complement of event A
( ) ( )APAnotP = 1Multiplication rule for independent events
( ) ( ) ( )BPAPBandAP =General multiplication rules
( ) ( ) ( )AgivenBPAPBandAP ,=
( ) ( ) ( )BgivenAPBPBandAP ,=Addition rule for mutually exclusive events
( ) ( ) ( )BPAPBorAP +=General addition rule
( ) ( ) ( ) ( )BandAPBPAPBorAP +=
Permutation rule( )!rn
n!rn,P
=
Combination rule( )!rnr!
n!rn,C
=
Chapter 5
Mean of a discrete probability distribution ( )= xxP
Standard deviation of a discrete probability distribution
( ) ( ) = xP2x
For Binomial Distributions
r = number of successes;p = probability of success; p1q =
Binomial probability distributionrn
qr
pr)!(nr!
n!P(r)
=
Mean np=
Standard deviation npq=
Chapter 6
Raw score x +=
Standard score
xz
=
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Chapter 7
Mean ofxdistribution x=
Standard deviation ofx distributionn
x=
Standard score forx n
x
z
=
Chapter 8
Confidence Interval
for ( )30nwhen
n
zx
n
zx cc +