AGS520S - AGRICULTURAL STATISTICS - 2ND OPP - JUNE 2025 :: NUST past examination papers between 2021 and 2025

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AGS520S - AGRICULTURAL STATISTICS - 2ND 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

AGS520S - AGRICULTURAL STATISTICS - 2ND OPP - JUNE 2025

1 Pages 1-10

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1.1 Page 1

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nAml BIA UnlVERSITY

OF SCIEnCEAnDTECHnOLOGY

FacultoyfHealthN, atural

ResourceasndApplied

Sciences

Schoool f NaturalandApplied

Sciences

Departmentof Mathematics,

StatisticsandActuariaSl cience

13JacksonKaujeuaStreet

PrivateBag13388

Windhoek

NAMIBIA

T: +264612072913

E: msas@nust.na

W:www.nust.na

QUALIFICATION : BACHELOR OF SCIENCEIN AGRICULTURE & BACHELOR OF SCIENCEIN

HORTICULTURE

QUALIFICATION CODE: 07BAGA & 07BHOR

COURSE: AGRICULTURAL STATISTICS

DATE: JULY 2025

DURATION: 3 HOURS

LEVEL: 5

COURSECODE: AGS520S

SESSION: 1

MARKS: 100

EXAMINER:

MODERATOR:

SECOND OPPORTUNITY: QUESTION PAPER

Mr. Jonas Amunyela, Mr. Polykarp Amukuhu

Mr. Andrew Roux

INSTRUCTIONS:

1. Answer all questions on the separate answer sheet.

2. Please write neatly and legibly.

3. Do not use the left side margin of the exam paper. This must be allowed for the

examiner.

4. No books, notes and other additional aids are allowed.

5. Mark all answers clearly with their respective question numbers.

PERMISSIBLE MATERIALS:

1. Non-Programmable Calculator

ATTACHEMENTS

1. Z distribution Table

2. T distribution table

3. Chi-square table

4. Formula sheet

This paper consists of 6 pages including this front page

1.2 Page 2

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QUESTION 1: MULTIPLE CHOICE QUESTIONS

[18 MARKS)

Evaluate the statements in each numbered section and select the most appropriate answer

1.1 _______

produce outcomes that come from a counting process, e.g. the

number of chickens present at the feeding area.

[2]

A.) Discrete random variable

B.) Continuous random variable

C.) Normal random variable

D.) Nominal random variable

E.) Ordinary random variable

1.2 __________

can be regarded as a nominal scale of measurement.

A.) Types of soil

[2]

B.) Age of individuals

C.) Weight of eggs

D.) Number of livestock

E.) None

1.3 When labels or names are being used to identify an attribute of each element, the

researcher is considering a:

[2]

A.) Nominal scale of measurement

B.) Ratio scales of measurement

C.) Qualitative data

D.) Quantitative data

E.) Interval scales of measurement

.,,

1.4 If set A and B forms a partition of the sample space S, which of the following is true

about set A and B?

[2]

a) P(A u B) = P(S)

b) P(A u B) = P(A) + P(B) - P(A n B)

c) P(S) = 0

d) P(A n B) = P(A) + P(B)

Agricultural Statistics (AGS520S) 2nd Opportunity JULY2025

1.3 Page 3

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1.5 Mathematical probabilities can have values

a) Between -1 and 1 inclusive

b) Corresponding to any positive real number

c) Between 0 and 1 inclusive

d) Quotients of positive whole numbers or zero

[2]

1.6 Supposed the events A and A are two complementary events. Which of the following

is not true about these two events?

a) P(A u A)= P(S)

b) 1- P(A) = P(A)

c)P(AUA)=l

d) P(A u A) -=I=l

[2]

1.7 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) independent probability

b) Conditional probability

c) Joint probability

d) Subjective probability

[2]

1.8 If the probabilities are respectively 0.20, 0.25 and 0.38 that a car stopped at a

roadblock will have faulty brakes, badly worn tyres, faulty brakes and badly worn

tyres. What is the probability that such a car will have faulty brakes or badly worn

tyres?

[2]

a) 0.09

0.29

0.07

0.45

1.9 Consider a bag containing 15 balls, of which 9 are green and 6 are white. In an

experiment 2 balls are drawn in succession, white followed by green.

[2]

Let A= {event of drawing a white ball}, Let B = {event of drawing a green ball}

What is the probability of drawing both white balls?

a) lh

b) 2/ 5

c) s/i4

d) 9hs

Agricultural Statistics (AGS520S) 2nd Opportunity JULY2025

1.4 Page 4

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SECTION B (Show all your working)

Question 2

[10 marks]

2.1 State whether each of the following is quantitative or qualitative variable. If it is

quantitative, state whether it is discrete or continuous.

a. Your crop variety

[2]

b. The number of tomatoes harvested per hector in the last 2 months.

[2]

c. The status of Foot-and-mouth disease (FMDV) in randomly selected farm animals

[2]

d. The weight of bags of dry beans from five different plots.

[2]

e. The soil types in 10 different plots

[2]

Question 3

(30 marks)

3.1 123 138 127 148 152 161 155 131 176

152 136 129 123 128 162 145 133 137 132

3.1.1 Determine the mode for the rainfall data.

[2]

3.1.2

Group the data into a grouped frequency distribution with a lowest class lower limit

of 120 mm and a class width of 10 mm. (NB include classes, frequency and relative

frequency)

[8]

3.1.3 What percentage of the rain fall was received between 120 mm to 130 mm? [1]

3.2 Cabbage is among the highest nitrates containing vegetarian food available in terms

of quantity. The following table presents the distribution of nitrates in grams that

was measured from 29 cabbages.

Nitrates contents

(in grams)

0-<9

9-<18

18-<27

27-<36

36-<45

Frequency

3.2.1 Estimate the mean nitrate for the cabbages

[3]

3.2.2 Estimate the median nitrate for the cabbages

[3]

3.2.3 Estimate the mode nitrate for the cabbages

[3]

Agricultural Statistics (AGS520S) 2nd Opportunity JULY2025

1.5 Page 5

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3.3 Two thousand randomly selected farmers were asked whether they have ever

shopped on the internet. The following table gives a two-way classification of the

responses

Have Shopped

Have never

Shopped

Male

400

800

Female

350

450

If one farmer is selected at random from these 2000 farmers, find the probability that this

farmer

3.3.1 has never shopped on the Internet

[2]

3.3.2 is a male

[2]

3.3.3 is male or has shopped on the internet

[2]

3.3.4 is female given that she has shopped on the internet

[2]

3.3.5 is male or female

[2]

Question 4

(17 marks)

4.1 It is assumed that a sampling error of no more than ±4 is desired along with 90%

confidence to determine a sample size appropriate to estimate the mean weights of

chicken eggs. Past data indicated that the standard deviations of the weight have been

approximately 22Kg for substantial period.

Calculate the sample size needed

[3]

4.2 An animal Farmer found that the sample average life of 30 specific blend of goats

tested was 10 years. The population standard deviation is known to be 5 years.

4.2.1 Construct and interpret a 90% confidence interval estimate for the true mean life of

all goats

[6]

4.3 An analytical chemistry lab is conducting quality control tests on a drug. A single

dosage of the drug should contain 8 mg of active ingredient. Of course, there will be

a small amount of variability due to imperfections in the production process, but the

mean of all dosages produced should be 8 mg. In 20 random dosages, the mean

amount of active ingredient is 7.7 mg with a standard deviation of 1.03 mg. Do the

Agricultural Statistics (AGS520S) 2nd Opportunity JULY2025

1.6 Page 6

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data suggest that the mean amount of active ingredient in all dosages produced is

different from 8 mg? use a = 0.05

[8]

QUESTION5

(25 marks)

5.4 A certain farm owner buys a particular battery for his tractor. He decides to stop

buying them if the mean life of these batteries is less than 24 months. A random

sample of 9 batteries yielded a mean life of 22 months with a standard deviation of 3

months.

Test whether the farm owner should stop buying these batteries using a 10% level of

significance.

[8]

5.5 The table below shows the heights (in meters) of a random sample of seven lemon

trees in Herta's Garden.

Trees

Height 1.05

0.99

1.2

1.1

1.5

0.98

0.95

5.5.1 Estimate the variance of the entire population of lemon trees in Herta's Garden with

a 99% degree of confidence.

[8]

5.5.2 Herta decides to continue growing lemon trees in her garden if the population

variance for the heights of these trees is more than 1.05 meters.

Should Herta continue growing lemons? Use 5% level of significance.

[9]

--------------------------------------------------------------------------------------------------------------------------

END OF QUESTION PAPER

Agricultural Statistics (AGS520S) 2nd Opportunity JULY2025

1.7 Page 7

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FORMULASHEET

= M L c[O.Sn-CF]

+ e

,rme

x-=-

"f,fx

tstat

x-µ

-s-

..Jn

2 _ (n-l)S 2

Xstat -

c,2

E(X) = LXiPi

P(X = x) = (:) pxqn-x

= b n"f,xy-"f,x"f,y

n"f,x2-("f,x) 2

= x, +x 2

n, +n 2

x- =-

"f,x

p±zfa}

Z = x-µ

= = P(X k) e-00x

Z=-a-x-µ

..Jn

°" 2 _ (fo-fe)2

Xstat - L, fe

a= y- bx

"f,(x·-x)

==--"--t

n-1

= s2 "f,(xi-x)2 Ii

n-1

1.8 Page 8

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Cumulative probabilities for POSITIVE z-values are shown below .

0.0

0.1

l 0.2

I 0.3

I 0.4

' 0.5

0.6

I 0.7

\\ 0.8

0.9

1.0

1.1

1.2

1.3

; 1.4

1.5

j 1.6

I 1.7 -

1.8

1 1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

i 2.8

I 2.9

3.0

3.1

3.2

3.3

3.4

.00

.5000

.5398

.5793

.6179

.6554

.69·15

.7257

.7580

.788·1

.8159

.8413

.8643

.8849

.9032

.9192

.9332

.9452

.9554

_954·1

.9713

.9772

.982·1

.986·1

.9893

.9_918

.9938

.9953

.9965

.9974

.9981

.9987

.9990

.9993

.9995

.9997

.01

.5040

.5438

.5832

.6217

.6591

.6950

.7291

.76-JI

.7910

.8"186

.8438

.8665

.8869

.9049

.9207

.9345

.9463

.9564

.9649

.9719

.9778

.9826

.9864

.9896

.9920

.9940

.9955

.9966

.9975

.9982

.9987

.9991

.9993

.9995

.9997

.02

.5080

.5478

.587"1

.6255

.6628

.6985

.7324

.7642

.7939

.8212

.8461

.8686

.8888

.9066

.9222

.9357

.9474 :

.9573

.9656

.9726

.9783

.9830

.9868

.9898

.9922

.9941

.9956

.9967

.9976

.9982

.9987

.9991

.9994

.9995

.9997

.03

.S-120

.SSH

.59-W

.6293

.6664

.7019

.7357

.7673

.7967

.8238

.8485

.8708

.8907

.9082

.9236

.9370

.9484

.9582

.9664

.9732

.9788

.9834

.9871

_990·1

.9925

.9943

.9957

.9968

.9977

.9983

.9988

.9991

.9994

.9996

.9997

.04

.5160

.5557

- .5948

.633·1

.6700

.7054

.7389

.7704

.7995

.8264

.8508

.8729

.8925

.9099

.925·1

.9382

.9495

_959·1

.967"1

.9738

.9793

.9838

.9875

.9904

.9927

.9945

.9959

.9969

.9977

.9984

.9988

.9992

.9994

.9996

.9997

.05

.5199

.5596

.5987

.6368

.6736

.7088

.7422

.7734

.8023

.8289

.8531

.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

.8051

.8315

.8554

.8770

.8962

.9131

.9279

.9406

.9515

.9608

.968-6

.9750

.9803

.9846

.9881

.9909

.9931

.9948

.9961

.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

.53"19

.5714

.6103

.6480

.6844

.7"190

.7517

.7823

.8106

.8365

.8599

.8810

.8997

.9162

.9306

.9429

.9535

.9625

.9699

.9761

.9812

.9854

.9887

.99B

.9934

.9951

.9963

.9973

.9980

.9986

.9990

.9993

.9995

.9996

.9997

.09

.5359

.5753

.6141

.6517

.6879

.7224

.7549

.7852

.8133

.8389

.862·1

.8830

.9015

.9177

_93·19

.9441

.9545

.9633

.9706

.9767

.9817

.9857

.9890

.99"16

.9936

.9952

.9964

.9974

.9981

.9986

.9990

.9993

.9995

.9997

.9998

1.9 Page 9

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Z-Table

The table shows cumulative probabilities for the standard normal curve.

Cumulativeprobabilitiesfor NEGATIVEz-valuesare shownfirst. SCROLL

DOWNto the 2nd pagefor POSITIVEz

-3.4

-3.3

-3.2

-3.1

-3.0

-~.9

-2.8

-2.7

-2.6

-2.5

-2.4

-2.3

-2.2

-2.1

-2.0

-1.9 ....

-1.8

I -1.7

I -1.6

l -1.5

. -1.4

-1.3

-1.2

-1.1

-1.0

I -0.9

•' -0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

.00

.0003

.0005

.0007

.oorn

.OOB

.0019

.0026

.0035

.0047

.0062

.0082

.0107

.0"139

.0"179

.0228

.0287

.0359

.0446

.0548

.0668

.0808

.0968

.1"151

.1357

.-1587

.1841

.2"1"19

.2420

-.2-743

.3085

.3446

.3821

.4207

.4602

.5000

.01

.0003

.0005

.0007

.0009

.00"13

.0018

.0025

.0034

.0045

.0060

.0080

.0104

.0136

.0174

.0222

.0281

_035·1

.0436

.0537

.0655

.0793

.0%1

.1131

."1335

.1562

.rn·14

.2090

.2389

.2709

.3050

.3409

.3783

.4168

.4562

.4960

.02

.0003

.0005

.0006

.0009

.0013

.0018

.0024

.0033

.0044

.0059

.0078

.0'102

.0132

.0170

.02'17

.0274

.0344

.0427

.0526

.0643

.0778

.0934

.11·12

.1314

.1539

.1788

.2061

.2358

.2676

.3015

.3372

.3745

.4·129

.4522

.4920

.03

.04

.0003 .0003

.0004 : .0004

.0006 .0006

.0009 .0008

.0012 .0012

.0017 .00'16

.0023 .0023

.0032 .003·1

.0043 .904·1

.0057 .0055

.0075 .0073

.0099 I .0096

.0129 .0125

.0166 .0162

.0212 .0207

.0268 .0262

.0336 ' .0329

.0-418 .0409

.0516 .0505

.0630 .06'18

.0764 .0749

.0918 .0901

.1093 I .1075

.1292 .127"1

.15'15 .1492

.1762 .1735

.2033 .2005

.2327 .2295

.2643 .26·1·1

.298"1 .2946

.3336 .3300

.3707 .3669

.4090 ! .4052

.4483 I .4443

.4880 : .4840

.05

.0003

.0004

.0006

.0008

.0011

.0016

.0022

.0030

.0040

.0054

.001·1

.0094

.0"122

.0158

.0202

.0256

.0322

_040·1

.0495

.0606

.0735

.0885

.1056

.125'1

.1469

.1711

.1977

.2266

.2578

.2912

.3264

.3632

.4013

.4404

.4801

.06

.0003

.0004

.0006

.0008

.0011

.0015

.0021

.0029

.0039

.0052

.0069

.0091

.0119

.0154

.0197

.-02..5. 0

.0314

.0392

.0485

.0594

.0721

.0869

.1038

.1230

.·1446

.-1685

.·1949

.2236

.2546

.2877

.3228

.3594

.3974

.4364

.4761

.07

.0003

.0004

.0005

.0008

.0011

.0015

.0021

.0028

.0038

.005·1

.0068

.0089

.0116

.0·150

.0192

.0244

.0307

.0364

.0475

.0582

.D708

.0853

.1020

.1210

.1423

.1660

.-1922

.2206

.2514

.2843

.3192

.3557

.3936

.4325

.4721

.08

.0003

.0004

.0005

.0007

.0010

.0014

.0020

.0027

.0037

.0049

.0066

.0087

.01-J3

.0146

.0188

.0239

_030·1

.0375

.0465

.057"1

.0694

.0838

.1003

.1190

.1401

.1635

.-1894

.2177

.2483

.28'10

_3·156

.3520

.3897

.4286

.4681

.09

.0002

.0003

.0005

.0007

.0010

.00'14

.00'19

.0026

.0036

.0048

.00(:4

.0084

.0·110

.0·143

.0183

.0233

.0294

.0367

.0455

.0559

.0681

.0823

.0985

.1170

."1379

.1611

.l867

.2148

.2451

.2776

.312"1

.3483

.3859

.4247

.4641

1.10 Page 10

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TABLE of CRITICAL VALUES for STUDENT'S t DISTRIBUTIONS

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

Column headings denote probabilities (a) above tabulated values.

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

0.687

0.686

0.685

0.684

0.683

0.682

0.681

0.679

0.678

0.677

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

1.308

1.307

1.306

1.305

1.304

1.303

1.296

1.292

1.290

1.289

1.288

1.287

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

1.651

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 0.0025 0.001 0.0005

63.656 127.321 318.289 636.578

9.925 14.089 22.328 31.600

5.841 7.453 10.214 12.924

4.604 5.598 7.173 8.610

4.032 4.773 5.894 6.869

3.707 4.317 5.208 5.959

3.499 4.029 4.785 5.408

3.355 3.833 4.501 5.041

3.250 3.690 4.297 4.781

3.169 3.581 4.144 4.587

3.106 3.497 4.025 4.437

3.055 3.428 3.930 4.318

3.012 3.372 3.852 4.221

2.977 3.326 3.787 4.140

2.947 3.286 3.733 4.073

2.921 3.252 3.686 4.015

2.898 3.222 3.646 3.965

2.878 3.197 3.610 3.922

2.861 3.174 3.579 3.883

2.845 3.153 3.552 3.850

2.831 3.135 3.527 3.819

2.819 3.119 3.505 3.792

2.807 3.104 3.485 3.768

2.797 3.091 3.467 3.745

2.787 3.078 3.450 3.725

2.779 3.067 3.435 3.707

2.771 3.057 3.421 3.689

2.763 3.047 3.408 3.674

2.756 3.038 3.396 3.660

2.750 3.030 3.385 3.646

2.744 3.022 3.375 3.633

2.738 3.015 3.365 3.622

2.733 3.008 3.356 3.611

2.728 3.002 3.348 3.601

2.724 2.996 3.340 3.591

2.719 2.990 3.333 3.582

2.715 2.985 3.326 3.574

2.712 2.980 3.319 3.566

2.708 2.976 3.313 3.558

2.704 2.971 3.307 3.551

2.660 2.915 3.232 3.460

2.639 2.887 3.195 3.416

2.626 2.871 3.174 3.390

2.617 2.860 3.160 3.373

2.611 2.852 3.149 3.361

2.607 2.847 3.142 3.352

2.603 2.842 3.136 3.345

2.601 · 2.838 3.131 3.340

2.596 2.832 3.123 3.330

2.576 2.807 3.090 3.290

2 Pages 11-20

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2.1 Page 11

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APPENDIX E: The Chi-Square Distribution

Page7 of7