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AGS520S-AGRICULTURAL STATISTICS - JAN 2020 |
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1 Pages 1-10 |
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1.1 Page 1 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION : BACHELOR OF AGRICULTURAL MANAGEMENT
QUALIFICATION CODE: 07BAGR
LEVEL: 5
COURSE CODE: AGS520S
COURSE NAME: AGRICULTURAL
STATISTICS
SESSION: JANUARY 2020
PAPER: THEORY
DURATION: 3 HOURS
MARKS: 100
SECOND OPPORTUNITY/SUPPLEMENTARY EXAMINATION QUESTION PAPER
EXAMINER(S)
MR. J Amunyela
MODERATOR: | MR.A.Roux
INSTRUCTIONS
Answer ALL the questions.
Write clearly and neatly.
Number the answers clearly.
Marks will not be awarded for answers obtained without showing
the necessary steps leading to them (the answers).
ATTACHMENT: formula sheet, t-table, z-table, chi-square
PERMISSIBLE MATERIALS
1. Non-Programmable Calculator without the cover
THIS QUESTION PAPER CONSISTS OF _7_ PAGES (Including this front page)
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1.2 Page 2 |
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SECTION A
QUESTION 1 [ 20 marks]
Write down the letter corresponding to your choice next to the question number.
1.1 The
central value
is the extent to which all the data values group around a
[2]
A.
central tendency
B.
subset of the population
C
measure of variability
D
variance
E.
sample point in the population
1.2 Which of the following is a property of the mean?
A.
Unique
B.
not affected by outliers
C.
there may be several means
D.
it is the sum of all observation
E.
All the above are measures of central tendency
[2]
1.3 The
is the value of the middle observation in a dataset that has
been ranked in increasing order.
[2]
A.
standard deviation
B.
mode
C.
range
D.
mean
E.
median
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1.3 Page 3 |
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1.4
Which of the following is true about normal distribution?
[2]
measures of dispersions are all equal
measures of central locations are all equal
the mean equals to the variance
parameters are equals to statistics
median equals to the variance
Which of the following is true in statistics?
[2]
the mean is not part descriptive statistics
same dataset cannot have different modes
x is the same as pp when the sample is small or large
Two datasets with the same mean may have completely different spreads
none
1.6 Consider a random variable X with the following probability distribution
X
2
8
12
14
17
P(X)
0.10
0.20
0.15
x
0.15
1.6.1 The probability P(X < 12) is:
[2]
0.10
0.30
0.45
0.15
none
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1.4 Page 4 |
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1.6.2 The value of x is
[2]
0.4
6.3
2.45
none
1.7 Which of the following statement is not a possible application of a poison
distribution:
[2]
A.
The number of cases of a disease in different farms in given time
B.
The number of mutations in set sized regions of a chromosome
C.
The number of particles emitted by a radioactive source each time
D.
The number of births per hour during a given day
E.
V(X) = np, for a poison random variable X
E.
all the above
1.8
The narrower the confidence interval,
[2]
A. the more precise it is
B. the less precise it is
C. the easier computations becomes
D. the larger the population
E. none
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1.5 Page 5 |
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1.9 Consider Hp: 4 = 55 and H,: uu < 55. lf we reject Hy we conclude that:
[2]
A.
the population mean is less than 55
B.
the population mean is more than 55
G
the population mean is equal to 55
D.
the population mean is not equal to 55
E.
all the above
SECTION B (Clearly show all your work)
Question 2 (33 marks)
Zul
Indicate whether the following statements are true (T) or false (F)
a.
The two tailed hypotheses testing for the mean has only one rejection region
[1]
b.
The variable weight is an example of a continuous random variable
[1]
c.
If A is an event that a seed sown will germinate and B is an event that a seed sown
will not germinate, then events A and B are mutual exclusive.
[1]
d.
The variable gender can be analysed as a nominal scale of measurement
[1]
e.
When performing a hypothesis testing for at least three means, we conduct a z-test.
[1]
f.
Ifn = 10, a = 5% the t-critical value is 1.2034 for a two tailed test
[1]
2.2 The following are the 400 soybean plant heights collected from a particular plot.
Plant
height(Cms)
8-12 | 13-17 | 18-22 | 23-27 | 28-32 | 33-37 | 38-42 | 43-47
No. of plants | 6
(fi)
17
25
86
125 77
55
9
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1.6 Page 6 |
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2.2.1 Estimate the average height of soybean
[4]
2.2.2 Estimate the median height of soybean
[4]
2.2.2 Estimate the modal height of soybean
[4]
2.2.3 Estimate the variance and standard deviation for the height of soybean
[5]
2.3 In certain district the incidence of rinderpest disease in cattle was found to be 8% (or
0.8) in a dairy farm consisting of 10 animals. If the incidence of rinderpest is assumed
to follow a binomial distribution, find
2.3.1 the average number of animals infected with the disease
[2]
2.3.2 the probability that exactly two animals are infected with the disease
[3]
2.3.3. the probability that at least 8 animals are infected
[5]
QUESTION 3 [19 MARKS]
3.1 It is assumed that a sampling error of no more than +3 is desired along with 95%
confidence to determine a sample size appropriate to estimate the mean weights of
lambs soon after birth for farm A. Past data indicated that the standard deviations of
the weight have been approximately 2Kg for substantial period.
Calculate the sample size needed
[3]
3.2
During December 2018, rainfall figures were recorded over 10 farms in the Khomas
region and the following information were obtained. s = 5.93, x = 29.6
a.) At the 5% level of significance test the hypothesis that the mean rainfall in Knhomas is
below 30mm.
[8]
b.) Construct a 95% confidence interval to estimate the mean rainfall amount for the
Khomas region.
[6]
c. What assumption must be made to be sure that the confident interval in b) above is
valid?
[2]
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1.7 Page 7 |
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QUESTION 4 [16 MARKS]
4.1 Suppose that we have the distribution of the yields (kg per plot) of two Ground nut
varieties from 5 plots each. The distribution may be as follows:
Variety 1
46
48
50
52
54
Variety 2
30
40
25
60
70
4.1.1 Can the researcher conclude that the average Yield for variety 1 is more than that of
variety 2? Use 5% significance level.
[9]
4.1.2 Is this a two tail or single tail hypothesis
[1]
4.1.3 Estimate a 95% confidence interval for the average difference in yields for the two
variety.
[6]
QUESTION 5 [12 MARKS]
5.1 The following data give the yield (in gm) from pigeonpea plants recorded over a
period of five consecutive years (2014-2018).
Time(years) | 2014
Yield
24.72
2015
20.25
2016
38.56
2017
74.72
2018
72.73
5.1.1 Fit by method of least squares a trend line equation for this dataset. (Use x =1,72...)
[12]
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1.8 Page 8 |
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FORMULA SHEET
M, =L+ c[0.5n—CF]
fme
ufx
n
X= t ZeC)oO
2
_ (n-1)s?
Xstat =
E(X) = Lixip;
P(X =x) = (()p*a"
_ nBxy-DxPy
nyx?2-(y x)?
<M t%
n +n,
g=
n
yo z*nP(=1?- )
E-
pz Pq
n
97 EE
oO
P(X =k)= e 9z9a x
Y=a+bx
My = L
Clfm—fm-1]
a
7 2fm—-fm-1—-fim+1
zZ=i34
vn
(py — Po) + Za( [PE + 7242)
2
ny
n2
= —11))sS2 < oe
x Sn-1
< eB —41))¢s2
x 1-Fn-1
Xst2 at — =D (foT-efe)”
V(X) = Xi — #)?pi)
__ Z7(0?)
E2
Z.. (py, —P,)-bs, ~,)
wa-a( tot]
m oN
_ D(xi-*)?
n-1
52 a Leics
n-1
=
Ss
x + ta, 1G@
(X,-—Xp) tt mat np
t _ (¥1-*2)-(H1-Ha)
s2 52
fed
ny 12
% = Yxp(x) and V(X) = Lm — *)? p(x)
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1.9 Page 9 |
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}
TABLE of CRITICAL VALUES for STUDENT'S t DISTRIBUTIONS
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Column headings denote probabilities (2) above tabulated values.
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10
£
12.
821
1.638
1.533
4
1.
14
;
3.747
:
3.365
2.998
2.764
18
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1.10 Page 10 |
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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
DOWN to the 2™ page for POSITIVE z
Zz.
.00
01
02
03
04
05
.06
7
08
.09
-3.4
0683
.0003
0003 {| .0003
0003
.0003
0003
0003
0003
0002
33
{0005
0005
0005
0004
0004
0004
0004
6004
-0004
0003
“32 | 0007 | .0007 | .0006 | .0006 | .0006 | .0006 | 0005 | .0005 | .0005 | .0005
341__[ 0010 _[ 000s {0009 | 0009 {0008 {0008 [0008 | 0008 (0007 | C007
30 | .0013 | 0013 | 0013 | 0012 | 0012 | 0011 [ 0011 | .0011 | .c010 [0010
“29 | 0019 | 0018 [| 0ois [| Ooty [| 0016 | 0076 | 0075 | 0015 | 0014 | 0014
28 | .0026 | .0025 | 0024 [| 0023 [| .0023 [ 0022 [ 0021 [ 0021 | .0020 | 0019
: Ake
0035:
0034
0033:
0032
0031 4 .0030
0023
0028
0027
.0026
26 | 0047 [0005 | 00as_ [004s | 00a1_[0040_[_o039 [0038 _[0037_| 0036_
-2:5
0062
0060
0059 | 0057 _ 0055
-0054
0052
0051 } .0049
0048
24
-0082
.0080
0078
0075
0073 {7 0071
0069
0068
0066
0064
2.3
0107
0104
0102
0099
0096 4 .0094
.0091
0089 | .0087
0084
2.2
0139
0136
0132
0129
0125
0122
.0119
0116
0113
110
2.1
.0179
0174
0170
0166 | 0162
0158 1 .0154
0150
0146
0143
—20_[_ oe [ tooo? _[ 012 [0207 [0202 ["o1s7 | o1s2 [ores [0183
r_-t9 | 0267 [| 0261 | 0274 | 0268| 0262 | 0256 [0250 | O24 | 0239| 02%
18 | 0359 | 0361{ 0344 | 0336| 0329 | 0322[ Osta | 0307 [0301 | 0294
rt | .0aae | 0036 | 007 | o4ie [0409 | 040i [0392 | 0364 [0375 | 0367
A
.0548
0537
-0526° 0516
0505 4 .0495
.0485
0475
0465
.0455
45 | 0668 | 0655 | .0643 | 0630 | de18 | 0606 | 0504 | 0582 | O571 | 0659_
-1.4
-0868
0793 | 0778 | 0764
0749
0735
0721
0708
0694
.0681
-1.3
.0968
0951
0934
0918
0901
0885
0869
0853 | .0838
0823 |
1.2
31151- 1131
1112
1093
1075
1056
1038
1020
-1003
0985
44 | i357 | 1385 [1314 | 1292 [1271 | 1251 [ 1230 | 1210 [ 1190 | 1170—
10 [-iee7_[ 1562 [139 [1515 |1492 | taea ["1aa6 [tas [1401 [1379
os | teat [tera | 1768 | 1762 [trae | 17ii [1605| 1660 [1635 [611
08 | 2119 | 2090 | 2061 | 2033 | 2005 | 1977 [ .1949 | 1922 | 1894 | .1867_
07 | 2420 | 2389 { 2368 | .2327 | 2096 | 2266 [| 236 | 2206 [ 2177 [ 2148 |
06 | 2743 | 2709 | 2676 | 2643 | 2611 | 2578 | 2646 | 2514 | 2483 [2461
0.5
3085
3050
3015
2981 | 2946
2912 | 2877
“2843
2810
2116
0.4
3446
3405
3372
3336 | .3300
3264
3228
3192
3156
3121
0.3
3821
3783
3t45
3707 | .3669
3632
3594
3557
3520
3483
4.2
4207
4168
4123
4090 | (4052
4013 | .3974
3936
2897
3859
-0.1
A602
A562
4522 4 4483 | 4443
4404 | .4364
4325
4286
A247
0.0
-50G0
A960
4920
4880
A840
4801
AT61
Af21
4681
4641
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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
‘dtp; 995 | 990 | 975 | 950
}
900 |ii .750 |: 500 | 250 |} 100 © oso | 025 | .o10 | .005
| 1 [0.00004 [0.00016 [0.00098 0.00393 [0.01579 [0.10153 {0.45494 |1.32330 [2.70554 | 3.84146 |5.02389 | 6.63490 [7.87944 |
_2 {0.01003 |o.02010 [0.05064 0.10259 {0.21072 |0.57536 [1.38629 |2.77259 (4.60517 [5.99146 [7.37776 (9.21034 |10.59663
| 3 [0.07172
[0.11483 [0.21580 [0.35185 [0.58437 [1.2
,
3 [2.36597 [4.10834 [6.25139 [7.81473 [9.34840 |11.34487 [1283816
Ta [0.20699 fo.29711 {0.48442 71072 |1.06362 {1.92256 [3.35669 [5.38527 | 7.77944 19.4873 |11.| 131.2746703[124.896026
|S [0.41174 [0.55430 (0.83121 [1.14548 |1.61031 |2.67460 [4.35146 | 6.62568 [9.23636 1.07050 | 12.83250 | 15.08627 | 16.74960
| 6 (0.67573 |0.87209 1.23734 |1.63538 [2.20413 [3.45460 |5.34812 |7.84080 | 10.6464 12.59159 | 14.44938 | 16.81189 [18.54758
98926 | 1.23904 1.68987 |2.16735 | 2.83311 [4.25485 | 6.34581 (9.03715 | 12.0170$ | 14.06714 | 16.01276 | 18.47531 [20.2774
“8 (1.3444) [1.64650 | 17973. {2.73264 {3.48954 [5.07064 [7.34412 | 10.2|1138.3861557 | 15.50731 | 1753455 20.09024 [21.95495
9 (1.73493 | 2.08790 2.70039 [3.32511 [4.16816 |5.89883 [8.34283 | 11.38875 | 14.68366 | 16.91898 | 19.02277 |21.66599 [23.58935
| 10 2.18586 [2.55821 (3.24697 [3.94030 [4.86518 6.73720 [9.34182 | 12.54886 |15.98718 | 18.30704 |2048518 |23.20925 [25.18818
| H1 [2.60322 |3.05348 [3.81575 [4.57481 (5.57778 [7.58414 [10|.13.3700469 |1170.27501 | 19.67514 |21.92005 |24.72497 |26.75685
[a2 [3o7ae2 [3.5787 [4.40579 {5.22603 [6.30380 [8.43842 {1.|314.4845400 |318.254935 |21.02607 {23.3366 | 26.21697 [2829952
| 43 [3.56503 }4.10692 |5.00875 [5.89186 |7.04150 [9.29907 | 12.3|9157.986391 | 19.81193 | 22.36203 |24.73560 27.6825 |29.81947,
| 14 [4.07467 [4.66043 5.62873 | 6.57063 | 7.78953 | 10.16531 | 1333927 | 17.1693 | 21.06414 |23.68479 | 26.1895 {9.14124 [3131935 |
[15 [4.60092 [5.22935 [6.26214 |7.26004 {8.54676 {11.3654 | 14.33886 | 18.24509 [2.30713 | 24.99579 |27.48839 |30.57791 |32.80132 |
| U6 [5.14221 [5.91221 [6.90766 (7.96165 [9.31224 {1.91222 | 15.33850 | 19.36886 | 23.54183 |26.| 282.8495356| 321.93999 [34.26719
{17 [5.69722 1640776 | 7.56419 | 8.67176 | 10.0|8152.1799193 | 16.33818 20.4868 |24.76904 |27.58711 |30.19101 | 3.40866 [35.71847
| 18 [6.26480 [7.01491 8.23075 9.39046 | 10.86494 | 13.67529 | 17.3790 : 21.60489 | 25.98942 |28.86930 |31.52638 |34.80531 |37.15645.
[19 [6.84397 [7.63273 [8.9065|2 10.11701 | 11.65091 | 14.5620 | 18.33765 |22.71781 |
| 20 [7.43384 [826040 [9.59078 [10.85081 | 12.44261 {15.4517 | 19.33743 | 23.82769 |28.41198 |31.41043 |34.16961 |37.56623 |39.99685.
[aa [8.03365 [8.89720 | 10.28290 !11.59131 , 13.23960 | 16.3438 | 20.33723 | 24.93478 29.61509 | 32.67057 | 35.47888 | 38.93217 [4140106
| 22 | 8.64272 | 9.54249 |10.98| 212.3332801 | 14.04149 | 17.23962 | 21.|326.3039277 |030.481328 33.9244 |36.78071 | 40.28936 |42.79565
| 23 19,26042 | 10.19572 |11.68855 , 13.09051 | 14.84796 | 18.13730 | 22.3688 |27.14134 "32.00690 |35.17246 |38.07563.(41.63840 (4.18128.
| 24 {9.88623 | 10.85|6132.640115 | 13.84843 | 15.65868 | 19.03725 |23.3673 | 28.24115 | 3.19624 | 36.41503 ; 39.36408 | 42.97982 |45.55851.
[25| 10.51965 | 11.52398 [13.1972 | 14.61 141 | 16.47341 | 19.93934 | 24.33659 | 2933885 | 34.38159 |37.65248 | 40.64647 | 44,31410 [46.92789
|26 {1.16024 {12.19815 /13.84390 | 15.37916 |17.29188 |20.84343 { 25.3646 | 30.43657| 35.56317 |38.88514 | 41.92| 435.1647168 | 48.28988
| 27 |11.80759| 12.8|7184.5570338 | 16.15140./ 18.1390 |21.74940 | 26.33634 |31.52841 36.74122 | 40.11327 (43.19451 | 46.96294 [49.64492
| 28 [1246134 { 13.56471 | 15.30786 | 16.92788 | 18.93924 |22.65716 | 27.33623 | 32,62049 | 37.91592 | 41.3714 |44.46079 | 48.27824 |50.99338
a9 [13.12115| 14.| 216.0547067 |817.570837 |19.76774 [23.5659 |28.33613 (33.71091 | 39.08747 {42.55697 | 45.7229 | 49.58788 [52.33562
} 30 | 13.78672| 14.95346 | 16.79077 | 18.4926 |20.59923 |24.47761 | 29.33603 | 34.7|9407.254602 |43.77297 | 46,97924 | 50.89218 | 53.67196
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