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AGS520S - AGRICULTURAL STATISTCS - 1ST OPP - NOV 2022 |
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1 Pages 1-10 |
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1.1 Page 1 |
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nAmtBIA unlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTYOF HEALTH,NATURAL RESOURCESAND APPLIEDSCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: BACHELOR OF AGRICULTURAL MANAGEMENT
QUALIFICATION CODE: 07BAGR
LEVEL: 5
COURSE CODE: AGS520S
COURSE NAME: AGR ICULTURAL
STATISTICS
SESSION: NOVEMBER 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
EXAMINER
FIRSTOPPORTUNITY EXAMINATION QUESTION PAPER
J. AMUNYELA
MODERATOR:
Mr A. ROUX
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
ATTACHMENT: Formula sheet, t-table, z-tables, chi-square table
PERMISSIBLEMATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 6 PAGES (Including this front page)
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1.2 Page 2 |
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SECTION A
(Write down the letter corresponding to your choice next to the question number)
Question 1[20 Marks]
1.1. When re-ordering, a shop owner is interested in ordering different milk flavour.
Looking at the sales data, which measure of central tendency is useful to him?
a) Mean
b) Median
c) Mode
d) All the above
[2]
1.2. A sample of a population is
a)
An experiment in the population
b) A subset of the population
c)
A variable in the population
d)
An outcome of the population
[2]
1.3. Which of the following is not a measure of central tendency in a statistical
distribution?
a) Mean
b) Median
c) Mode
d) Standard deviation
[2]
1.4. Fill in the blank to make the following sentence true. "The ______
of a
particular outcome is the number of times it occurs within a specific sample of a
population."
a) Frequency
b) Variance
c) Mean deviation
d) Distribution
[2]
1.5 Which of the following is NOT a possible probability?
a) 25/100
b) 1.25
c) 1
d) 0
[2]
2
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1.6 Mathematical probabilities can have values
a) Between -1 and 1 inclusive
b) Corresponding to any positive real number
c) Between O and 1 inclusive
d) Quotients of positive whole numbers or zero
[2]
1.7 A student is chosen at random from a class of 16 girls and 14 boys. What is the
probability that the student chosen is not a girl?
a)S/15
b)7/15
c) 0.35
d) 0
[2]
1.8 If you believe that the probability of purchasing a new tractor is dependent on
getting a new higher paying job next year, the probability of purchasing the tractor is
an example of:
a) Simple probability
b) Conditional probability
c) Joint probability
d) Subjective probability
[2]
1.9 The sampling technique whereby members of the population are placed in an array
and every tenth member is selected is an example of:
[2]
a)
Random sampling
b)
Systematic sampling
c)
Cluster sampling
d)
Stratified sampling
1.10 You are doing research on farm personnel-orderlies, chief technicians, scientific
officer, and implement operator. You want to be sure you draw a sample that has
elements in each of the personnel categories. You want to use probability sampling.
An appropriate strategy would be:
[2]
a)
Simple random sampling
b)
Quota sampling
c)
Cluster sampling
d)
Stratified sampling
3
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1.4 Page 4 |
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SECTION B (Show all your working)
Question 2 [40 Marks]
2.1 Consider the following maximum temperature data for 10 winter days recorded in
Otavi.
24,37,26,46,58,30,32, 13, 12,38,
Calculate the following:
2.1.1 The mean.
[2]
2.1.2 The median.
[2]
2.1.3 The standard deviation.
[5]
2.2 As part of disease control system the veterinary department has recorded the
number of cases per farm related to food and mouth disease in various regions of
the country during year 2021.The table below present the data
10 31 21 60 12 30 42 45 50 50 36
43 52 64 40 44 40 55 48 46 59 58
51 61 47 53 41 31 47 48 33 59 53
62 49 35 48 26 36 24 62 32 41 20
2.2.1 Using classes 10 to less than 20, 20 to less than 30, and 30 to less than 40, construct
a frequency distribution table for the data.
[7]
2.3 Let X be the random variable with the following probability distribution
I ~-05
I :.,5
4
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2.3.1 Estimate the mean for a random variable X
[3]
2.3.2 Estimate the variance and the standard deviation for a random variable X
[6]
2.3.3 Find P(X > 4)
[2]
2.4 The incidence of disease in a guava garden is such that 20% of the guava trees in the
garden have the chance of being infected. If a random sample of six guava trees is
selected,
2.4.1 what is the probability that at least three trees will have the symptoms of the
disease
[5]
2.4.2 what is the probability that at most two trees will have the symptoms of the disease
[4]
2.4.3 what is the probability that exactly two trees will have the symptoms of the disease
[2]
2.4.4 what is the average number of the infected trees
[2]
Question 3 [20 Marks]
3.1 The Auditing procedures require you to have 95% confidence in estimating the
population proportion of sales invoices with errors to within± 0.07 of the true
population proportion. The results from past month indicated that the largest
proportion has been not more than 0.15. Find the sample size
[4]
= 3.2 In a particular variety of wheat, leaf area is normally distributed with meanµ
= 100 cm2 , and standard deviation (J" 9 cm2 • If a random sample of 36 trees is
considered, calculate the probability that the average area of the leaves is less than
100 cm 2
[3]
3.3 Milk yields of dairy cows generally follow a normal distribution. The monthly yield of
a particular breed (Breed X) is believed to be normally distributed with a standard
= deviation (J" 45 litres when grazed without dietary supplements. Several farmers
start feeding their Breed X cattle on experimental supplement. The monthly yield of
a random sample of 35 of these cows shows a mean yield x = 220 litres per month.
5
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3.3.3 Construct and interpret a 95% confidence interval for estimating the actual milk
yields of dairy cows
[6]
3.4 The following data are of milk fat yield (kg) per month from 17 Holstein cows:
27, 17,31,20,29,22,40,28,26,28,34,32,32,32,30,23,25
3.4.1 Use the data to construct a 98% confidence interval for the average milk fat yield of
all Holstein cows
[7]
Question 4 [20 Marks]
4.1 In a certain cattle-raising region of the country, it had become a practice among
some farmers to feed their Breed X cows a protein supplement which, when fed to
other dairy breeds, had never been known to do anything except increase milk
yields. The monthly milk yields of a random sample of 50 protein-supplemented
cows were recorded. The mean value x was 209 litres and the population standard
deviation was believed to be 40 litres.
4.1.1 Is there any reason to believe that the protein supplement has increased the average
milk yield of Breed X cows to more than 200 litres? Use a = 5%
[10]
4.2 The eggs of the Cuckoo family have a length which is approximately normally
distributed with mean ofµ = 20 mm. The Cuckoo is a nest parasite, especially on
nests of the Warbler family, the Sylviidae. Fifteen Cuckoo eggs were taken at random
from nests of the Marsh Warbler. The length of these eggs (units mm) were,
19
20
20
20
20
20
21
21
21
21
21
22
22
22
22
4.2.1 Is there any evidence to suggest that the average length of the Cuckoo eggs in Marsh
Warbler nests is different from the general population? Use a= 2%
[10]
6
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FORMULASHEET
= + Me l c[O.Sn-CF]
fme
x-=-
2,[x
n
= x-µ
tstat -s-
Jn
2 _ (n-1)5 2
Xstat - crZ
= b n2,xy-2,x2,y
n2,x2-(2,x) 2
x, +x,
Jr=---
n, +n 2
x-=-
r,x
n
z2p(1-P)
n= £2
p±z)¥
Z = x-µ
CT
P(X = k) = e-eex
x!
= Mo l + c[tm-fm-il
2fm- fm-1 - fm+1
Z=-a-x-µ
rn
2 _ "(fo-fe)2
Xstat - L, fe
a= y-bx
s 2 =--rt,-(x·-x) 2
n-1
= s2 r,(xi-x)z fi
n-1
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1.8 Page 8 |
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TABLE of CRITICAL VALUES for STUDENT'S t DISTRIBUTIONS
Column headings denote probabilities (a) above tabulated values.
d.f. 0.40
1 0.325
2 0.289
3 0.277
4 0.271
5 0.267
6 0.265
7 0.263
8 0.262
9 0.261
10 0.260
11 0.260
12 0.259
13 0.259
14 0.258
15 0.258
16 0.258
17 0.257
18 0.257
19 0.257
20 0.257
21 0.257
22 0.256
23 0.256
24 0.256
25 0.256
26 0.256
27 0.256
28 0.256
29 0.256
30 0.256
31 0.256
32 0.255
33 0.255
34 0.255
35 0.255
36 0.255
37 0.255
38 0.255
39 0.255
40 0.255
60 0.254
80 0.254
100 0.254
120 0.254
140 0.254
160 0.254
180 0.254
200 0.254
250 0.254
inf 0.253
0.25
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703
0.700
0.697
0.695
0.694
0.692
0.691
0.690
0.689
0.688
0.688
0.687
0.686
0.686
0.685
0.685
0.684
0.684
0.684
0.683
0.683
0.683
0.682
0.682
0.682
0.682
0.682
0.681
0.681
0.681
0.681
0.681
0.679
0.678
0.677
0.677
0.676
0.676
0.676
0.676
0.675
0.674
0.10
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.309
1.309
1.308
1.307
1.306
1.306
1.305
1.304
1.304
1.303
1.296
1.292
1.290
1.289
1.288
1.287
1.286
1.286
1.285
1.282
0.05
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.696
1.694
1.692
1.691
1.690
1.688
1.687
1.686
1.685
1.684
1.671
1.664
1.660
1.658
1.656
1.654
1.653
1.653
1.651
1.645
0.04
7.916
3.320
2.605
2.333
2.191
2.104
2.046
2.004
1.973
1.948
1.928
1.912
1.899
1.887
1.878
1.869
1.862
1.855
1.850
1.844
1.840
1.835
1.832
1.828
1.825
1.822
1.819
1.817
1.814
1.812
1.810
1.808
1.806
1.805
1.803
1.802
1.800
1.799
1.798
1.796
1.781
1.773
1.769
1.766
1.763
1.762
1.761
1.760
1.758
1.751
0.025
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.040
2.037
2.035
2.032
2.030
2.028
2.026
2.024
2.023
2.021
2.000
1.990
1.984
1.980
1.977
1.975
1.973
1.972
1.969
1.960
0.02
15.894
4.849
3.482
2.999
2.757
2.612
2.517
2.449
2.398
2.359
2.328
2.303
2.282
2.264
2.249
2.235
2.224
2.214
2.205
2.197
2.189
2.183
2.177
2.172
2.167
2.162
2.158
2.154
2.150
2.147
2.144
2.141
2.138
2.136
2.133
2.131
2.129
2.127
2.125
2.123
2.099
2.088
2.081
2.076
2.073
2.071
2.069
2.067
2.065
2.054
0.01
31.821
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.453
2.449
2.445
2.441
2.438
2.434
2.431
2.429
2.426
2.423
2.390
2.374
2.364
2.358
2.353
2.350
2.347
2.345
2.341
2.326
0.005
63.656
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.744
2.738
2.733
2.728
2.724
2.719
2.715
2.712
2.708
2.704
2.660
2.639
2:626
2.617
2.611
2.607
2.603
2.601
2.596
2.576
0.0025 0.001 0.0005
127.321 318.289 636.578
14.089 22.328 31.600
7.453 10.214 12.924
5.598 7.173 8.610
4.773 5.894 6.869
4.317 5.208 5.959
4.029 4.785 5.408
3.833 4.501 5.041
3.690 4.297 4.781
3.581 4.144 4.587
3.497 4.025 4.437
3.428 3.930 4.318
3.372 3.852 4.221
3.326 3.787 4.140
3.286 3.733 4.073
3.252 3.686 4.015
3.222 3.646 3.965
3.197 3.610 3.922
3.174 3.579 3.883
3.153 3.552 3.850
3.135 3.527 3.819
3.119 3.505 3.792
3.104 3.485 3.768
3.091 3.467 3.745
3.078 3.450 3.725
3.067 3.435 3.707
3.057 3.421 3.689
3.047 3.408 3.674
3.038 3.396 3.660
3.030 3.385 3.646
3.022 3.375 3.633
3.015 3.365 3.622
3.008 3.356 3.611
3.002 3.348 3.601
2.996 3.340 3.591
2.990 3.333 3.582
2.985 3.326 3.574
2.980 3.319 3.566
2.976 3.313 3.558
2.971 3.307 3.551
2.915 3.232 3.460
2.887 3.195 3.416
2.871 3.174 3.390
2.860 3.160 3.373
2.852 3.149 3.361
2.847 3.142 3.352
2.842 3.136 3.345
2.838 3.131 3.340
2.832 3.123 3.330
2.807 3.090 3.290
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1.9 Page 9 |
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Z-Table
The table shows cumulative probabilities for the standard normal curve.
Cumulative probabilities for NEGATIVE z-values are shown first. SCROLL
DOWNto the 2nd page for POSITIVEz
Lz
.00
.01
.02
.03
.04
-3.4 .0003 .0003 .0003 .0003 .0003
-3.3 .0005 .0005 .0005 .0004 .0004
-3.2 .0007 .0007 .0006 .0006 .0006
-3.1 .00·10 .0009 .0009 .0009 .0008
-3.0 .0013 .00·13 .0013
I I I -2.9 .0019 .0018 .0018
' -2.8
I -2.7
.0026 .0025 .0024
.0035 .0034 .0033
-2.6 .0047 .0045 .0044
.0012
.0017
.0023
.0032
.0043
.00·12
.00·15
.0023
.0031
.0041
-2.5 .0062 .0060 .0059 .0057 .0055
-2.4 .0082 .0080 .0078 .0075 .0073
-2.3 .0107 .0'104 .0102 .0099 .0096
-2.2 .0139 .OB6 .0132 .0129 .0·125
-2.1 .0'179 .0174 .0170 .0166 .0162
-2.0 .0228 .0222 .0217 .0212 .0207
r.
'•
-1.9
-1.8
-1.7
.0287
.0359
.0446
.028'1
_035·1
.0436
.0274
.0344
.0427
.0268
.0336
.04'18
.0262
.0329
.0409
j -1.6 .0548 .0537 .0526 .05'16 .0505
-1.5 .0668 .0655 .0643 .0630 .06'18
-1.4 .0808 .0793 .0778 .0764 .0749
-1.3 .0968 .095'1 .0934 .09'18 .0901
-1.2 .115'1 .'113"1 -1112 .1093 .1075
-1.1 .1357 .1335 .1314 .1292 :1271
-1.0 .1587 .'1562 .1539 .'1515 .1492
l -0.9 .1841 .!8'14 .1788 .1762 .1736
.1 -0.8 .21'19 .2090 .206'1 2033 .2005
I I I I I -0.7 .2420 .2389 .2358 .2327 .2296
.0.6 .2743 .2709 .2676 .2643 .2611
.0.5 .3085 .3050 .3015 .2981 .2946
.0.4 .3446 .3409 .3372 .3336 .3300
-0.3 .3821 .3783 .3745 .3707 .3669
.0.2 .4207 .4168 .4'129 .4090 .40-52
-0.1 .4602 .4562 .4522 .4483 .4443
i 0.0
.5000 .4960 .4920 .4880 .4840
.05
.06
.0003 .0003
.0-004 .0004
.0006 .0006
.0008 .0008
.0011 .0011
.0016 .0015
.0022 .0021
.0.030 .0029
.0040 .0039
.0054 .0052
.0071 .0069
.0D94 .009·1
.0122 .01·19
.0158 .0·154
.0202 .0'197
.0256 .0250
.0322 .0314
.04CY1 .0392
.0495 .0485
.0606 .0594
.0735 .0721
.0885 .0869
.1G56 .1038
.1251 :1230
.'l469 .'1446
.171'1 .1685
.1977 .1949
.2266 .2236
.2578 .2546
.29'12 .2877
.3264 .3228
.3632 .3594
.4013 .3974
.4404 .4364
.4801 .4761
...
.07
.0003
.0004
.0005
.0008
.001'1
.0015
.002·1
.0028
.0038
.0051
.0068
.0089
.0116
.0·150
.0192
.0244
.0307
.0384
.0475
.0582
.0708
.0853
.1020
.1210
.1423
.'1660
.'1922
.2206
.2514
.2843
.3192
.3557
.3936
.4325
.4721
.08
.0003
.0004
.0005
.0007
.00'10
.0014
.0020
.0027
.0037
.0049
.0066
.0087
.0113
.0'146
.0188
.0239
.0301
.0375
.0465
.057·1
:0694
.0838
.'1003
.1'190
.140'1
.'1635
.'1894
.2177
.2483
.2810
.3'156
.3520
.3897
.4286
.4681
.09
.0002
.0003
.0005
.0007
.OO'IO
.00'14
.0019
.0026
.0036
.0048
.0064
.0084
.0·110
.0143
.0'183
.0233
.0294
.0367
.0455
.0559
.0681
.0823
.0985
.1170
.1379
.161'I
.1867
.2148
.2451
.2776
.312'1
.3483
.3859
.4247
.4641
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1.10 Page 10 |
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Cumulative probabilities for POSITIVE z-values are shown below .
z
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
' 1.4
I 1.5
1.6
1.7
I 1.8
1.9
; 2.0
... 2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
.00
.5000
.5398
.5793
.6179
.6554
.6915
.7257
.7580
.7881
.8159
.8413
.8643
.8849
.9032
.9192
.9332
.9452
.9554
.9641
.9713
.9772
.9821
.986'1
.9893
.9918
.9938
.9953
.9965
.9974
.9981
.9987
.9990
.9993
.9995
.9997
.01
.5040
.5438
.5832
.6217
.6S91
.6950
.7291
.76'11
.7910
.8186
.8438
.8665
.8869
.9049
.9207
.9345
.9463
.%64
.9649
.9719
.9778
.9826
.9864
.9896
.9920
.9940
.9955
.9966
.9975
.9982
.9987
_999·1
.9993
.9995
.9997
.02
.5080
.5478
.5871
.6255
.6628
.6985
.7324
.7642
.7939
.82·12
.8461
.8586
.8888
.9066
.9222
.9357
.9474
.9573
.9656
.9726
.9783
.9830
.9868
.9898
.9922
.994"1
.9956
.9957
.9976
.9982
.9987
.9991
.9994
.9995
.99~17
.03
.5120
.5517
.5910
.6293
.6664
.10·19
.7357
.7673
.7967
.8238
.8485
.8708
8907
.9082
.9236
.9370
.9484
.9582
.9664
.9732
.9788
.9834
.9871
.9901
.9925
.9943
.9957
.9968
.9977
.9983
.9988
.999"1
.9994
.9996
.9997
.04.
.5'160
.5557
.5948
.6331
.6700
.7054
.7389
.7704
.7995
.8264
.8508
.8729
.8925
.9099
.925"1
.9382
.9495
.9591
.967"1
.9738
.9793
.9838
.9875
.9904
.9927
.9945
.9959
.9969
.9977
.9984
.9988
.9992
.9994
.9996
.9997
.05
.5'199
.5596
.5987
.6368
.6736
.7088
.7422
.7734
.8023
.8289
.853'1
.8749
.8944
.9115
.9265
.9394
.9505
.9599
.9678
.9744
.9798
.9842
.9878
.9906
.9929
.9946
.9960
.9970
.9978
.9984
.9989
.9992
.9994
.9996
.9997
.06
.5239
.5636
.6026
.6406
.6772
.7123
.7454
.7764
.805'1
.83"15
.8554
.8770
.8962
.9"131
.9279
.9406
.9515
.9608
.9685
.9750
.9803
.9846
.9881
.9909
.9931
.9948
.996"1
.9971
.9979
.9985
.9989
.9992
.9994
.9996
.9997
.07
.5279
.5675
.6064
.6443
.6808
.7157
.7486
.7794
.8078
.8340
.8577
.8790
.8980
.9147
.9292
.9418
.9525
.9616
.9693
.9756
.9808
.9850
.9884
.9911
.9932
.9949
.9962
.9972
.9979
.9985
.9989
.9992
.9995
.9996
.9997
.08
.5319
.57"14
.6"103
.6480
.6844
.7"190
.7517
.7823
.8"!06
.8365
.8599
.8810
.8997
.9162
.9306
.9429
.9535
.9625
.9699
.9761
_93·12
.9854
.9887
.99"13
.9934
.9951
.9963
.9973
.9980
.9986
.9990
.9993
.9995
.9996
.9997
.09
.5359
.5753
.6'141
.6517
.6879
.7224
.7549
.7852
.8'133
.8389
.8621
.8830
.90'15
.9177
.93'19
_944·1
.9545
.9633
.9706
.9767
.9817
.9857
.9890
.9916
.9936
.9952
.9964
.9974
.9981
.9986
.9990
.9993
.9995
.9997
.9998
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2 Pages 11-20 |
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2.1 Page 11 |
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APPENDIX E: The Chi-Square Distribution
~t(,>-'.
1 --r-;;;;-·i-~:-~1~:-soo~: -r:asii-T !-DIO~, idJ\\p-:99s -i---_990
.100
.025
I I ! I i i I I 0.00004 r-;00016 fo.ooo98 0.00393 0.01579 [0.10153 ) 0.45494 j 1.32330 j 2.70554 3.84146 j 5.02389 f 6.63490 7.87944
L .1 I ! ~i 2_ i?·0_1_003 omo10 0.05064 0 !0259
I '! i I ! r 0.57536 1.38629 f2_772;9 4 6051_7}5.99146 ;,37776 9.2!034 . 10 59663
! 3_10.07172 [o.il483 !0.21580_\\Q.35l85 !(l.58437 ~53
j2.36597 _14.l0834 __j6.25139_(781473 j9.34840 _iu.34487f!2_-838161
r r 1 114 , 4 10.20699 0.2971 I 10.48442 10.71072 1.06362 11.92256 3.35669 15.38527 17.77944 i9.48773 1I 1.14329 j 13.27670 .86026 1
f I i ! ! ii S
j 0.41174
,
rl0.55430
I 0.83121
I
~1, .14548
..
1.61031
,
2.67460
I
i!,<i,3j 5146
6.62568
l
1' 9.23636
: I l.07050
•
!I 12.83250
j
!
15.08627
16.74960
1
----·-----r---------------I---------·---c---·-·-i··----·--------i!-------!·-·-·--!--·--------.----·· jr!·-67---·j!'D0·..-69-78·5-97•2-36···j!r··01--.·.8·2-.·73.-2-9·00-94····Jj1-l·1-.-6.·2.8-.3_-9.7.8_.37_4__,!_-21-.·.16-6-3·75-3-35·8-·--\\!,22-,.82·30-3·4·11·13·--\\j-34r.,-42-55-4--16r80·5---j6-5,..334•1588112
i 7.84080 10.644M 12.59159 14.44938
-·--··•·--.---·----·-1-·-·--.-..--.-. --·-··---------
!9.03715 12.01704, 14.06714116.01276
j 16.81189
I··1-8-.-4·7-5-31
!r1-~-:-5-4758
jl0.2777_4
1
i ! f i ! s 1.34441 f 1.64650 2.17973 12.13264 J3.48954 f5.01064 [7.34412 flo.21ss5 13.36l51 1s.so131!11.53455120.09024 !21.95495
! ! i4J6816i i 9 Jl.TI49312.08790 {?0039 !3.32511
5.89883 18,34283 JI l.38875 14.68366: 16.91898 jl9.02277 ~9123.58935
! ! ·10-·12.15586 12.55821 ·13.24697-i3,94030 .. 'l4.86518 ..T6.73720--·19.34182 !12.54886-!15.98718 18.30704•120.48318 l23.20925 j25.18818.
~!2.60322
13.05348 13.81575 j4.57481 is.57778 i1.s8414 ~34100 j13-10069 f!7.21so1 i19.67514 i21.92005 j24.7249; fu.156s5:
ii. ! JJ:oi1sr2is··10:s1::;:;4·1Jj:,9-r;;:22w:i
r! ,4I ! 13 3.56503 14.10692 5.00875 Js.89186
14.07467 -14,66043 !s.62873 )6.57063
! i i6~jo:is·;;·-18.43842 11.34032 14 s4s40J1&.S:i;jjs"Fi~o216U:02116·?1r;j:23s~~2939532··1666-
! i i ! 17 f .04150 9_29901 112.33976 is.98391 19.81193 22.36203 24.73560 ~129.81941;i
17.78953 [J0.16531 [13.J3927i11.11693i21.06414 l23.68479l26.11895j29.14124'31.31935·
! ! \\ rs 14.60092 _fs:22935 j 6.26214 j 7.26094 js.54676 11.03654·114.33886 18.24509 jn.30113 ~9
I j21.48&39 130.51791 32.80132
!16!5.14221 15.81221 JG.90766 j7.96165 j9.31224 111.91222 ~s5oj19.368&6!23.S4:83
\\26.29623 [2s.84535-i31:99993r"-26119
i i :
'
11
'15.69722
.------16.4077.656419
.
•
_18.67176
'
!1 10.08519
1112.19193
'
16.33818 i 20.48868
!.
'I24.76904
·121.ss111
!. .10.19101
fo.40866
I
'35.71847
,.,;.:,,
l
! i ! J i ! ~! I 18 6.26480 11.01491 s.23075 9.39046 _!10.86494 fo.61529 fl7.3379o 21.60489 !25.98942 28.86930
34.80531 37. 15645
! I I ! ! i i p [_19 6.84397 )7.63273 8.90652 ['io.11101 t.65091 14.56200 tS.33765 j 22.111s1 21.20351 30.14353 32_s5233 j 36.19os1 j3&.58226.
L ! i I I i i ! .i 20 r-43384 f'ii604o i9.59078 10.s5081 12.44261 15.45111 19.33743 23.82769 28.41198 : 31.41043 34.16961 37.56623 9.99685
I I i i I l 13 I 21 j8.03365 fs.891_20 10.28290
! if3.23960 1.r6.H138 20 33723 24.93478 29.61s09. n.67057'! 35.47888 38.93217 J41.40106
I f l I I .I : 22 fs.54212 9.54249 1ni.98232 12.33801 114.04149 11.23962 2u3104 : 26.03921 : 30.81328
40.28936 42.79565
/nf 1 11 i 9.26042- l0.19572 ~
3~09051 114.84796 Gs.J;;;;;;-~sf2ii.i134
13 132.00690 s.17246 i38 o7563 i4t.63840144.18128
i ~ r 19.88623 110:85636 : 12.40115 113.84843 115.65868 19.03725r23.33673 128.24115 133.19624 : 36.41503 13936408 [42.97982 145.55851
l ! r ! i 25 flo.s1965 jll-52398 : 13.11972 !14.6114I 116.47341 19.93934 24.33659 i29.33885 -!~4.:3_8_15193?.65248_ ~0.64647 i44~314J(Jr46.92789
i26l 1 r r 13 .r I 1.16024 rru9815_ 13.84390; 15_.37916117.29188 20.84343 125.33646130.43457 35.56317 s.88514 41.9231: f45.~1_68 ,48.28988
1
! ! i ! i i f21-fli.so159,/ 12.87850 14.57338 16.15140 18.11390 j21.14940 26.336J4 j 3t.52841 36.74122 40.11n1 j43.19451 ~!49-64492-.
fl8TJ'2A6134rl3:56471
I ! 15.30786 16.92788i18.93924122.65716 j27.33623 !32.62049 ["n9isi?:fii·:;;:;1·,i·r«~46079~!48.27s24
iso.99338
! i 1 ! i29i13.121 )5 114.25645 16.04101 111.10837 19.76774 23.56659 28.336!3 [33.11091 139.08747
I J45.12229 49.58788 rs2.33562
! 30 j 13.78672·114.9534611~.79077 Jl8.49266 fio.m23 J24.4776I /29.33603 j34.79974 !40.25602 !43.77297 \\46.97924 l.50.892l8 f.sJ.67196
Page7 ol7