FAS411S - FUNDAMENTALS OF AGRICULTURAL STATISTICS - 1ST OPP - JUNE 2025 :: NUST past examination papers between 2021 and 2025

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FAS411S - FUNDAMENTALS OF AGRICULTURAL STATISTICS - 1ST OPP - JUNE 2025

1 Pages 1-10

1.1 Page 1

1.2 Page 2

1.3 Page 3

1.4 Page 4

1.5 Page 5

1.6 Page 6

1.7 Page 7

1.8 Page 8

1.9 Page 9

1.10 Page 10

2 Pages 11-20

2.1 Page 11

2.2 Page 12

FAS411S - FUNDAMENTALS OF AGRICULTURAL STATISTICS - 1ST OPP - JUNE 2025

1 Pages 1-10

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1.1 Page 1

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nAmlBIA unlVERSITY

OF SCIEnCE Ano TECHnOLOGY

FACULTY OF COMMERCE, HUMAN SCIENCES AND EDUCATION

DEPARTMENT OF TECHNICAL AND VOCATIONAL EDUCATION AND TRAINING (TVET)

QUALIFICATION: NUST BRIDGING PROGRAMME -TVET AGRICULTURE

SPECIALISATION

QUALIFICATION CODE: 04NBTA

LEVEL: 4

COURSE CODE: FAS411S

COURSE NAME: FUNDAMENTALS

OF AGRICULTURAL STATISTICS

SESSION: JUNE 2025

DURATION: 3 HOURS

PAPER: 1

MARKS: 100

EXAMINER(S)

FIRST OPPORTUNITY EXAMINATION QUESTION PAPER

MS. E MATALI

MODERATOR: Dr TEOFILUS SHIIMI

INSTRUCTIONS

1. This question paper consists of SECTION A and SECTIONB questions

2. For SECTIONA write down the letter corresponding to the correct option for each

question

3. For SECTION B is essay questions

4. Answer all questions in blue or black ink

ATTACHMENT: Formula sheet, t-table, z-table, chi-square table

PERMISSIBLE MATERIALS: 1. Non-Programmable Calculator without the cover

THIS QUESTION PAPER CONSISTS OF _11_ PAGES {Including this front page)

1.2 Page 2

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SECTION A

QUESTION 1

[10 marks]

Write down the letter corresponding to your choice next to the question number.

1.1. When re-ordering, a farm owner is interested in ordering different animal feed.

Looking at the consumption data, which measure of central tendency is useful to

him?

a) Mean

b) Median

c) Mode

d) All the above

(1)

1.2. Which of the following is NOT a possible probability?

a)25/100

b) 1

c) -1

d)O

(1)

1.3. 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

(1)

1.4. An _____

is a process that generate well defined outcomes.

a) Simple random sampling

b) Experiment

c) Joint probability

d) Subjective probability

(1)

1.3 Page 3

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1.5. Events A and Bare said to be mutually exclusive if

a) A intersection Bis not an empty set

b) A union Bis empty set

c) An intersection Bis empty set

d) None

(1)

1.6. A pig is chosen at random from a pig house of 16 males and 14 females. What is

the probability that the pig chosen is not a male?

a) 8/15

b) 7/15

c) 0.35

d) 0

(1)

1.7. Which of the following represents the numeric characteristics of the population.

a) A statistics

b) A parameter

c) A variance

d) A distribution

(1)

1.8. -----

is the likelihood of an outcome of event

a) Sampling

b) Experiment

c) Cluster sampling

d) Probability

(1)

1.9. Fill in the blank to make the following sentence true. "The frequency of a particular

outcome is the number of times it occurswithin a specific_ of a population."

a) Frequency

b) Variance

c) Sample

d) Distribution

(1)

1.4 Page 4

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1.10. 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

(1)

SECTION B

QUESTION 2 {TRUE OR FALSEQUESTIONS)

[10 marks]

2.1. Indicate whether each of the following statements is true or false, and provide a

justification for your answer.

[10 marks]

2.1.1 The standard deviation measures the central tendency of a dataset.

2.1.2. The probability of an event is always between O and 1.

2.1.3. The values of a chi-square can be zero or positive but never negative

2.1.4. A larger sample size reduces the accuracy of an estimate.

2.1.5. The cumulative frequency of the last class in a frequency distribution is equal to the

total number of observations.

2.1.6. The range of a data set is calculated by adding the highest and lowest values.

2.1.7. A scatter plot is useful for visualizing the correlation between two quantitative

variables.

2.1.8. A small p-value in hypothesis testing suggests that the null hypothesis should be

rejected.

2.1.9. A histogram is used to display the relationship between two variables.

2.1.10. The coefficient of variation is expressed as a percentage.

1.5 Page 5

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1.6 Page 6

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SECTIONC

QUESTION 3

3.1. A fair coin is tossed twice. The outcome of each toss is recorded.

[80 marks]

[15]

3.1.1. Draw a tree diagram to represent all possible outcomes.

(5)

3.1.2. Find the probability of:

a) Getting two heads

(2)

b) Getting at least one tail

(3)

c) Getting exactly one head

(3)

3.2. The following relates to the weights of 36 female students in Namibia University of

Science and Technology. The data were recorded to the nearest kilogram.

[8]

3.2.1. Using classes 120 to less than 130, 130 to less than 140, and 140 to less than 150...,

construct a frequency distribution table for the data. NB your frequency distribution table

must include; less than cumulative frequency, percentage frequency and class midpoint.

138

146

168

146

161

164

158

126

173

150

140

138

142

135

173

150

132

147

176

147

144

136

163

135

150

125

148

120

153

149

150

125

152

154

140

145

157

144

165

135

3.3. Over the course of 3 hours 55 batches of harvested crops arrive at a processing facility.

The processing facility has been recording the delay in the arrival of each batch, measured

in minutes. The number of minutes they were late is shown in the grouped frequency table

below.

[12]

1.7 Page 7

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Minutes late

0-10

10-20

20-30

30-40

40-50

50-60

Frequency

3.3.1. Estimate the mean late arrival time for the batches of crop

(4)

3.3.2. Estimate the variance for late arrival time for the batches of crop

(4)

3.3.3. Estimate the standard deviation for late arrival time for the batches of crop

(4)

3.4. Make a Stem-and-Leaf Plot of the following set of data sets:

[9]

a) 7, 10, 11, 12, 11, 11, 13, 8, 22, and 23

(3)

b) 1.6, 2.4, 1.8, 2.3, 1.9, 1.6, 2, 4.1, and 4

(3)

c) 121, 90, 97, 96, 110, 118, 128, and 120

(3)

3.5. Suppose that there were 120 students in the classroom and that they could be classified

as follows:

[14]

3.5.1. Complete the contingency table by calculating the missing values: a, b, c, and d. (4)

Gender

Male

Female

Total

HAIR COLOUR

Brown

Not Brown

Total

120

1.8 Page 8

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3.5.2. Find the probability that a randomly selected:

a) P(A}=

b) P(AnB} =

c) P(AUB}=

d) P(BnC} =

e) P (NnB} =

(10)

(2)

3.6. A trade union claims that the average hourly rate paid to domestic cleaners

throughout the country is only N$2,85. To test this claim, a survey amongst a sample

of 250 domestic farm workers was conducted. The sample mean was found to be

N$3,03. Assume the population standard deviation of hourly rates paid to domestic

farm workers is N$1,00. Test the hypothesis at 5% significance level that the average

hourly rate paid to domestic farm workers is indeed N$2,85.

[12]

3.7. An agriculture clothing store analyzed the value of purchases made on credit card

by a sample of 25 credit card customers. The sample mean was found to be N$165,45

with a sample standard deviation of N$38,60. Construct a 95% Cl for the actual mean

value of credit card purchases at this store.

[1O]

END OF PAPER [100]

1.9 Page 9

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FORMULA SHEET

l;'(X)= Exp,

C) P(X = x) = pxq• -

b = ,,r -Exty

n •Al -(l: ,:)l

,T=--X +X

n +lit

pl:

· _ 'C' le -Ir)~

X ca, - l., I.

= -I>.

P,)-(,, 1-,T)

= ,1 sl

E{.r -

tt-1

L1u,n-1 -)(ii

1.10 Page 10

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2-Table

The table shows cumulative probabilities for the standard normal curve.

Cumulative probabilities for NEGATIVEz-values are shown first. SCROLLDOWN to the 2nd

page for POSITIVEz

.00

.01

.J.4 .0003 .0003

-3.3 .0005 .0005

.J.2 .0007 .0007

-3.1 .0010 .0009

-3.0 .0013 .0013

I -2.9 .0019 .0018

-2.8 .0026 .0025

:i.1 .0035 .00~

-2.6 .0047 .0045

-2.5 .0062 .0060

-2..4 .0082 .0080

' -2.3 .0107 .0104

-2.l. .0139 .0136

.2.1 .0179 .0174

-2.0 0228 .0222

I I -1.9 .0287 ,0281

I -1.8 .0359 .0351

-1.7 .0446 .OJ.36

-1.6 -~8

.0537

-1.5 .0668 .0655

-1.4

-1.3

.0808 .0793

.0968 .0951

-1.2 .1151 .1131

-1.1 .1357 .1335

.,.o .1587 .1562

.0.9 .1841 .1814

.0..8 .2119 .2090

--0.7 .2.d20 2389

.0.6 .2743 .2709

.0.5 .3085 .3050

.0.4 -~6

.3409

.0.3 .3821 .3783

.0.2 .4207 .4168

.0.1 .4602 .4562

f 0.0 .5000 .4960

.02

0003

.0005

.0000

.0009

.0013

0018

.0024

.0033

.0044

.0059

0078

.0102

0132

.0170

0217

.027J

.0344

.0427

0526

.0643

ona

.0934

1112

1314

1539

1788

2061

2358

2676

.3015

.3372

.3745

.4129

4522

4920

.03

OOJ3

.0004

.0006

.0009

0012

.0017

.0023

0032

.0043

.0057

.0075

,0099

.0129

.0166

.0212

.0268

.0336

.0418

.0616

.0630

.0764

09t8

.1093

1292

. 1515

.1762

2033

2327

2643

.2981

.3336

.3707

.4090

4483

4880

.04

.0003

.0004

.0006

.0008

.0012

.0016

.0023

.0031

.0041

.0055

.0073

.0096

.0125

.0162

.0207

.0262

.0329

.Oit09

.0505

.0618

.0749

_09()1

.1075

.1271

.1492

.1736

..2005

.2296

.2611

.29J6

.3300

.3W3

.4052

.4443

.de.to

.05

.0003

.0004

.0006

.0008

.0011

.00-16

.0022

.0030

.0040

.0054

.0071

.0094

.0122

.0158

0202

.0156

.0322

.0401

.0495

.0606

.0735

.0885

.1056

.1251

.1469

.1711

.1sn

,2266

.2578

.2912

.326-i

.3632

.4013

.4404

.4801

.06

.C003

.0004

.0006

.0008

.0011

.0015

.0021

.0029

.0039

.0052

.0069

.0091

.0119

.OIS4

.0'197

.0250

.03ld

.0392

-~85

.0594

.on1

.0069

.1038

.1230

.1446

.1685

.1949

.2236

.2546

.28TT

.3228

.3594

3974

.4364

0:761

.07

0003

.0004

.0005

.0008

.0011

.0015

.0021

.0028

.0038

.0051

.0068

.0089

.0116

.0150

.0192

.0244

.0307

.0384

.0475

.0582

.0700

.0853

.1020

.1210

.1423

.1660

.1922

.22~

.2514

.2843

.3192

..3557

.3936

.4325

,'1721

- --

.08

.0003

.0005,

.0007

.0010

.0014

.0020

.0027

.0037

.00!9

.0066

.0087

.0113

.0146

.0188

.0239

.0301

.0375

.0465

_0:,,1

.0694

.0838

.1003

.1190

.1401

.1635

.189-$

.2177

.2483

.2810

.3156

.3520

.3897

.4286

.4681

.09

.0002

.0003

.0005

J)007

.0010 I

.0014 II

.0019

I 0026

.0036

.0048 I•

I•

.0064

_()()84

0110 I'

.0143-

0183

.0233

.0294

.0367

.0455

I .0559

.0681

,0823

.0985

.1170

.1379

.1611

.1867

,2148

.2451

.2776

.3121

.3483

.3859

.42.47

.4641

2 Pages 11-20

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2.1 Page 11

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0.0

0.1

0.2

0.3

0.4

0.5

0.6

t 0.7

f 0.8

I 0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

I 1.8

i 1.9

r 2.0

2.1

2.2

i 2.3

f 2.5

2.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

J.4

Cumulative probabilities for POSITIVEz-values are shown below.

__ ,

-- -~-

.00

.01

.02

.03

.04

.05

.06

.07

.08

.5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319

.5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714

.5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103

.6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6400

.655d .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844

.6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190

.7257 7291 .7324 .7357 .7389 .1<122 .7454 .7486 .7517

.7580 .761'1 .7642 .7673 .7704 .7T34 .n64 .TT94 .7823

.7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106

.8159 .8186 8212 8238 .8264 .8289 .8315 ,8340 .8365

.8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599

.8643 .8665 .8686 .S708 .8729 .8749 .8770 .8790 .8810

.8849 .8869 .8888 .~7

.8925 .8944 .6962 .8980 .8997

.9032 .9:>49 .9066 .9082 .9099 .9115 .9131 .9147 .9162

.9192 .CJl.07 .9222

I .93.32 I .9345 I .9357

.9452 .9463 .9"474

I I .9564 .9564 .9573

,9641 .9649 .9656

.9236

.9370

.9-l84

.9582

.9664

.9251

.9382

.9495

.9591

.9671

.9265

.9394

.9505

.9599

.9678

.9279

.9406

.9515

.9608

.9686

.9292

.9418

.9525

.9616

.9693

.9306

.9429

.9535

.9625

.9699

.9713 .'!'119 .9726 .9732 .9738 .9744 .9750 .9756 .9761

.9772 .9778 9783 .9788 .9793 .9798 .9803 .9808 .9812

.9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9654

.9861 .9864 .9868 .9871 .9675 .9878 .9881 .9884 .9887

.9893 .9896 .9898 .9901 .9904 .99£l6 .9909 .9911 .9913

.9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934

.9938

.9953

.9965

.9940

.9955

.9966

.9941

.9956

.9967

.9943 .9945

I .9957 .9959

.99!xl .9969

.994~

.9960

.9970

.9948

.9961

.9971

.9949

.9962

.9972

.9951

.9963

.9973

.9974 .9975 .9976 .9.977 .9977 .9978 .9979 .9979 .9980

.9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986

.9987 .9987 ,9987 .9988 .9988 .9989 .9989 .9989 .9990

.9990 .9991 9991 .9991 .9992 .9. 992 .9992 .9992 .9993

.9m .9993 .9994 .9994 .9994 .999J .9994 .9995 .9995

.9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996

- -- .999-7

.9997

.9997 ,9997

.9997

-·-

.9997

.09

.5359

.5753

.6141

.6517

.6879

.7224

.7549

.7852

.8133

.8389

.8621

.8830

.9015

.9177

.9319

.9441

.9545

.9633

.9706

.97fil

.9817

..9857

.98ro

.9916

.9936

.9952

.9964

.997.S

.9931

.9986

.9990

.9993

.9995

.9997

.9998

---

2.2 Page 12

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TABLE of CRITICAL VALUES for STUDENT'S t DISTRIBUTIONS

Column headings denote probabilities (a) above tabulated values.

d.f.

I 18

' 100

I 120

140

160

180

200

' 250

inf

0.40 0..25

0.325 1.000

0.289 0.816

0.277 0.765

0.271 0.741

0.267 0,727

0.265 0.718

0.263 0.711

0.262 0.706

0.261 0.703

0.260 0.700

0.260 0.697

0.259 0.695

0.259 0.694

0.258 0.692

0.258 0.691

0.268 0.690

0.267 0.889

0.257 0.688

0.257 0.687

0.257 0.686

0.256 0.686

0.256 0.685

0.256 0.684

0256 0.684

0..256 0.683

0..2.56 0.683

0.683

0.256 0,682

0.265 0.682

0265 0.682

0.255 0.682

0.265 0.682

0.255 0.681

0.254 0.679

0.264 0.678

0.254 0.677

0.254 o.sn

0.254 0.676

0.264 0.676

- 0,263 - 0.674

0.10

3.078

1.886

1.838

1-633

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

1.32-8

1.325

1.323

1.321

1.319

1.318

1.316

1.315

1.314

1.313

1.311

1.310

1.309

1.308

1.307

1.306

1.305

1.304

1.303

1,296

1,292

1.290

1.289

1.288

1.287

1.266

1.286

t.282

0,05

6.314

2.92-0

2.353

2.132

2.016

1.943

1.895

1.860

1.833

1.8t2

1.796

1.782

1.n1

1.761

1.763

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

f.699

1.6. 97

1.696

1.694

1.692

1.691

1.690

1,688

1.687

1.686

1.665

1.684

1.671

1.664

1.660

1.658

1.656

1.654

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.nJ

1.769

1.766

1.763

1.762

1.781

1.760

1.768

1.751

0.025 0.02 0.01

12.706 15.89-4 31.821

4.303 4.849 6.965

3.182 3,482 4.541

2.776 2.999 3.747

2 671 2 767 3.365

2.447 2.612 3,143

2.365 2.517 2.998

2.306 2.449 2.896

2..262 2.398 2.821

2..228 2.359 2.764

2.201 2.328 2.718

2.179 2.303 2.681

2.160 2.282 2.650

2.146 2.264 2.624

2.131 2.249 2.602

2.120 2.235 2.683

2.110 2.224 2.567

2.101 2.214 2.562

2.093 2.205 2.5S9

2.086 2.197 2.528

2.080 2.16-9 2.618

2.074 2.183 2.608

2.069, 2.1n 2.600

2.064 2.172 2.492

2.060 2.167 2.485

2.056 2.162 2.479

2.052 2.158 2.473

2.048 2.154 2.467

2.045 2.150 2.462

2.042 2.147 2.457

2.040 2.144 2,463

2.037 2.141 2.449

2,035 2.138 2.«5

2.032 2.136 2.'441

2.030 2.133 2.'438

2.028 2.131 2.434

2.026 2.129 2.431

2.024 2.127 2.428

2.023 2.125 2,426

2,021 2,123 2423

2.000 2.099 2..390

1.990 2.088 2.374

1.984 2.081 2.364

1.980 2.076 2.358

1.977 2.073 2.353

1.975 2.071 2.350

1.873 2.069 2.347

1.972 2,(~7 2.345

1.969 2.065 2.341

-- . - 1.960 2.054 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.TT9

2.n1

2.763-

2.756

2.760

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

2.807

2.603

2.601

2.696

2.576

0.0025 0.001 0..0005 11

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 M94 6,869

4.317 5.208 6.969

4.029 4.786 5.408

3.833 4.601 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

3.262

3.222

3.197

3.686

3.646

3.610

I 4.016

3.965

3.922

3.17'4 3.579 3.883

3.163 3,552 3.850

3.136 J.527 3.819

3.119

3.104

3.091

3.078

3.505

3.485

3.467

3.450

I 3,792

J.768

3.745

3.ns ;,

3.067 3.435 3.707

3.057 3..421 3.689 II

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

2.996

2.990

3.348

3.340

3.333

3.601

I 3.591

3.582

2.985 3.326 3.674

2.980 3.319 3.566 ,I

2.976 3.313 3.668

2.971 3.307 3.651

2.915 3.232 3.-460

2.887 3.195 3..C16

2.871 3.17'4 3.390

2.860 3.160 3.373

2.852 3.1-49 3.361

2.847 3.142 3.352

2.642 3.136 3.346

2.838 3.131 3.340

2.832 3.123 3.330

-- 2.807 3.090 3.290