AGS520S - AGRICULTURAL STATISTICS - 1ST OPP - NOVEMBER 2023 :: NUST past examination papers between 2020 and 2024

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AGS520S - AGRICULTURAL STATISTICS - 1ST OPP - NOVEMBER 2023

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 - 1ST OPP - NOVEMBER 2023

1 Pages 1-10

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1.1 Page 1

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nAmlBIA UnlVERSITY

OFscienceAnorecHnOLOGY

FacultyofHealthN,atural

ResourceasndApplied

Sciences

Schoool f NaturalandApplied

Sciences

Departmenot f Mathematics.

StatisticsandActuarialScience

13JacksonKaujeu~Street T: •264 612072913

Prlvate Bag13388

E: msas@nust.na

Windhoek

W: www.nust.nJ

NAMIBIA

QUALIFICATION: BACHELOR OF AGRICULTURAL MANAGEMENT

QUALIFICATION CODE: 07BAGR

LEVEL: 5

COURSE: AGRICULTURAL STATISTICS

COURSE CODE: AGS520S

DATE: NOVEMBER 2023

SESSION: 1

DURATION: 3 HOURS

MARKS: 100

EXAMINER:

MODERATOR:

FIRSTOPPORTUNITY:EXAMINATION QUESTIONPAPER

Mr. Jonas Amunyela

Mr. Andrew Roux

INSTRUCTIONS:

1. Answer all questions on the separate answer sheet.

2. Pleasewrite 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 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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SECTION A

(Write down the letter corresponding to your choice next to the question number)

Question 1

(22 Marks]

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?

[2]

a) Mean

b) Median

c) Mode

d) All the above

1.2. A sample of a population is

[2]

An experiment in the population

b) A subset ofthe population

A variable in the population

d) An outcome of the population

1.3. Which of the following is a measure of dispersion in a statistical distribution?

[2]

a) Mean

b) Median

c) Mode

d) Standard deviation

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

outcome is the number of times it occurs within a specific ___ of a population."

a) Frequency

[2]

b) Variance

c) Sample

d) Distribution

Agricultural Statistics (AGS520S)

pt Opportunity-November 2023

1.3 Page 3

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1.5 Which of the following is NOT a possible probability?

[2]

a) 25/100

b) 1

c) -1

d) 0

1.6 Mathematical probabilities can have values

[2]

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

1.7 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?

[2]

a)8/15

b)7/15

c) 0.35

d)O

1.8 An______

is a process that generate well defined outcomes.

[2]

a) Simple random sampling

b) Experiment

c) Joint probability

d) Subjective probability

1.9 -------

is the likelihood of an outcome of event

[2]

a) Sampling

Experiment

Cluster sampling

Probability

1.10 Events A and Bare said to be mutually exclusive if

[2]

a) A intersection Bis not an empty set

b) A union Bis empty set

A intersection B is empty set

None

Agricultural Statistics (AGS520S)

l' t Opportunity-November 2023

1.4 Page 4

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1.11 Which of the following represents the numeric characteristics of the population. [2]

A statistics

A parameter

A variance

A distribution

SECTION 8 (Show all your working}

Question 2

(37 Marks]

2.1 Consider the following daily maximum temperature data for 10 winter days recorded

in Oshana region.

24, 30, 20, 36,52, 30, 32, 13, 22, 38,

Calculate the following:

2.1.1 The mean.

[2]

2.1.2 The median.

[2]

2.1.3 The standard deviation.

[4]

2.2 As part of the disease control system the veterinary department has recorded the

number of cases per farm related to food and mouth disease in Khomas region

during year 2022.The table below present the data.

10 31 21 60 12 30 42 45 50 36

43 52 64 40 44 40 55 48 46 58

51 61 47 53 41 31 47 48 33 53

62 49 35 48 26 36 24 62 32 20

2.2.1 Using classes 10 -< 20, 20 -< 30, 30 -< 40, and so on, construct a frequency

distribution table for the data.

[6]

2.3 Let X be the random variable with the following probability distribution.

I ~.OS

I: 25

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

[4]

Agricultural Statistics (AGS520S)

l't Opportunity-November 2023

1.5 Page 5

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2.3.3 Find P(X < 4)

[2]

2.4 Suppose it is known that 5% of adults who take a certain medication experience a

negative side effect. If a random sample of 100 adult patients was taken, use a

binomial probability distribution to find the probability that:

2.4.1 More than two adult patients will experience the negative side effects

(4]

2.4.2 Exactly three adult patients will experience the negative side effects

[2]

2.4.3 At least two adults will experience the negative side effects

(SJ

2.5. How many adults are expected to have the side effects

[3]

Question 3

(25 Marks)

3.1 The Auditing procedures require you to have 99% confidence in estimating the

population proportion of sales invoices with errors to within ± 0.09 of the true

population proportion. The results from the past month indicated that the largest

proportion has been not more than 0.12. Find the sample size

[3]

= = 3.2 If Xis normally distributed with the meanµ 20 and standard deviation a 4,

determine the following probability:

a) P(X s; 10)

[2]

b) P(X 10)

[3]

c) P(16 s; X s; 24

(4]

3.3 Maize yields generally follow a normal distribution. The yearly yield of a particular

= maize is believed to be normally distributed with a standard deviation a

45 kg when grown in sandy-loam soil. Several farmers in the same area start

applying fertilizers on their small plots. The yearly yield of a random sample of 35 of

= these plots shows a mean yield x 220 kg per year.

3.3.3 Construct and interpret a 90% confidence interval for estimating the actual yearly

maize yields from these plots.

[6]

3.4 The following data are of milk fat yield (kg) per month from 9 Holstein cows:

27, 17,31,20,29,22,40,28,26

Agricultural Statistics (AGS520S)

1st Opportunity-November 2023

1.6 Page 6

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3.4.1 Use the data to construct a 99% confidence interval for the average milk fat yield of

all Holstein cows

(7]

Question 4

[16 Marks]

4.1 In a certain cattle-raising region of the country, it had become a practice among

some farmers to feed their Brahman 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 41 protein-supplemented

cows were recorded. The mean value x was 205 litres and the population standard

deviation was believed to be 40 litres.

4.1.1 Test at 5% significance level to determine if protein supplement has increased the

average milk yield of Brahman cows to more than 200 litres?

(8)

4.2 The eggs of the Cuckoo family have a length which is approximately normally

distributed with mean less than 20 mm. The Cuckoo is a nest parasite, especially on

nests of the Warbler family, the Sylviidae. Ten Cuckoo eggs were taken at random

from nests of the Marsh Warbler. The length of these eggs (units mm) were,

4.2.1 Is there any evidence to suggest that the average length of the Cuckoo eggs in Marsh

= Warbler nests is less than 20 mm? Use a 2%

(8)

*******************END OF EXAMINATION QUEST1ON PAPER******************

Agricultural Statistics (AGS520S)

1st Opportunity-November 2023

1.7 Page 7

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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

I -3.1

-3.0

-2.9

-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

: -1.5

I -1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

.Q.1

0.0

.00

.0003

.0005

.0007

.0010

.0013

.0019

.0026

.0035

.0047

.0062

.0082

.0107

.0139

.0179

.0228

.0287

.0359

.0446

.0548

.0668

.0808

.0968

.1151

.1357

.1587

.1841

.2119

.2420

.2743

.3085

.3446

.3821

.4207

.4602

.5000

.01

.0003

.0005

.0007

.0009

.00·13

.0018

.0025

.0034

.0045

.0060

.0080

.0104

.0136

.0174

.0222

.0281

.0351

.0436

.0537

.0655

.0793

.0951

.1'131

.1335

.1562

.18'14

.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

.0217

.0274

.0344

.0427

.0526

.0643

.0778

.0934

.1112

.1314

.1539

.1788

.2061

.2358

.2676

.3015

.3372

.3745

.4129

.4522

.4920

.03

.0003

.0004

.0006

.0009

.0012

.0017

.0023

.0032

.0043

.0057

.0075

.0099

.0129

.0166

.0212

.0268

.0336

.04'18 I

.0516

.0630 I

.0764

.0918

.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

.0409

.0505

.0618

.0749

.090'1

.1075

.1271

.1492

.1736

.2005

.2296

.261'1

.2946

.3300

.3669

.4052

.4443

.4840

.05

.0003

.0004

.0006

.0008.

.0011

.0016

.0022

.0030

.0040

.0054

.0071

.0094

.0122

.0158

.0202

.0256

.0322

.0401

.0495

.0606

.0735

.0885

.1056

.1251

.1469

.1711

.1977

.2266

.2578

.2912

.3264

.3632

.4013

.4404

.4801

.06

.0003

.0004

.0006

..0008

.00·11

.0015

.0021

.0029

.0039

.0052

.0069

.0091

.0119

.0154

.0197

.0250

.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

.0051

.0068

.0089

.01'16

.0150

.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

.0010

.0014

.0020

.0027

.0037

.0049

.0066

.0087

.0113

.0146

.0188

.0239

.0301

.0375

.0465

.0571

.0694

.0838

.1003

.1190

.1401

.1635

.189-:1

.2177

.2483

.2810

.3156

.3520

.3897

.4286

.4681

.09

.0002

.0003

.0005

.0007

.0010

.0014

.0019

.0026

.0036

.0048

.0064

.0084

.0'110

.0143

.0'183

.0233

.0294

.0367

.0455

.0559

.0681

.0823

.0985

.1170

.1379

.1611

.1867

.2'148

2451

.2776

.3121

.3483

.3859

.4247

.4641

1.8 Page 8

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Cumulative probabilities for POSITIVE z-values are shown below.

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

I 0.0

.5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .531!:I .5359

0.1

.5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .5753

0.2

.5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .614'1

0.3

.6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517

0.4

.6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879

0.5

i 0.6

I 0.7

.6915

.7257

.7580

.6950

.rn·,

.7611

.6985

.7324

.7642

.7019

.7357

.7673

.7054

.7389

.7704

.7088

.7422

.7734

.7123

.7454

.7764

.7157

.7486

.7794

.7190

.75'17

.7823

.7224

.7549

.7852

i 0.8

.7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133

I 0.9

.8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389

1.0

.8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621

! 1.1

.8643 .8665 .8586 .8708 .8729 .8749 .8770 .8790 .8810 .8830

t 1.2

.8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997

I 1.3

.9032 -~

,9{166 .9082 .9099 .9115 .9131 .9147 .9162

I I I I I I I 1.4

I I I .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306

I 1.5

.9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429

.9015

.9177

.9319

.9441

I 1.6

.9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545

1.7

.9554 .9564 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633

1.8

.9641 .9649 .9656 .9654 .9671 .9678 .9686 .9693 .9699 .9706

1.9

.9713 .9719 .9726 .9732 .9738 .9744 .9750 .97:,6 .9761 .9767

2.0

.9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817

2.1

.9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857

2.2

.9861 .%64 I .98-68 .9871 .9875 .9878 .9881 .9884 .9887 .9890

2.3

.9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .!:1913 .9916

2.4

.9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936

2.5

.9938 .9940 .994'1 .9943 .9945 .9946 .90.A8 .9949 .9951 .9952

2.6

.9953 .9955 .9956 .9957 .9959 .9960 .9961 .9. 962 .9963 .9964

2.7

.9965 .9966 .9967 .9958 .9969 .997D .9971 .9972 .9973 .9974

2.8

.9974 .9975 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .9981

2.9

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

3.0

.9987 .9987 .9987 .9988 .S988 .9989 .9989 .9989 .999D .9990

3.1

.9990 .999·1 .9991 .9991 .9992 .9992 .9992 .9992 ' .9993 .9993

3.2

.9993 .9993 .9994 .9994 .9994 .9994 .9994 .9995 .9995 .9995

f 3.3

I 3.4

.9995

.9997

.9995

.9997

.9995

.9997

.9996

.9997

.9996

.9997

.9996

.9997

.9996

.9997

.9996

.9997

.9996

.9997

.9998

1.9 Page 9

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TABLE of CRITICAL VALUES for STUDENTS 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

3'1 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 0254

120 0.254

140 0254

160 0254

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

0.687

0.686

0.685

0.684

0.683

0.682

0.681

0.679

0.678

o.6n

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

1292

1.290

1.289

t.288

1.287

1.286

1.285

1282

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.TT3

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.n6

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

1.9n

1.975

1.973

1.9n

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

2.9n

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

127.321

14.089

7.453

5.598

4.TT3

4.317

4.029

3.833

3.690

3.581

3.497

3.428

3.372

3.326

3.286

3.252

3.222

3.197

3.174

3.153

3.135

3.119

3.104

3.091

3.078

3.067

3.057

3.047

3.038

3.030

3.022

3.015

3.008

3.002

2..996

2.990

2.985

2.980

2.976

2.971

2.915

2.887

2.871

2.860

2.852

2.847

2.842

2.838

2.832

2.807

0.001

318289

22.328

10.214

7.173

5.894

5.208

4.785

4.501

4297

4.144

4.025

3.930

3.852

3.787

3.733

3.686

3.646

3.610

3.579

3.552

3.527

3.505

3.485

3.467

3.450

3.435

3.421

3.408

3.396

3.385

3.375

3.365

3.356

3.348

3.340

3.333

3.326

3.319

3.313

3.307

3.232

3.195

3.174

3.160

3.149

3.142

3.136

3.131

3.123

3.090

0.0005

636.578

31.600

12.924

8.610

6.869

5.959

5.408

5.041

4.781

4.587

4.437

4.318

4.221

4.140

4.073

4.015

3.965

3.922

3.883

3.850

3.819

3.792

3.768

3.745

3.725

3.707

3.689

3.674

3.660

3.646

3.633

3.622

3.611

3.601

3.591

3.582

3.574

3.566

3.558

3.551

3.460

3.416

3.390

3.373

3.361

3.352

3.345

3.340

3.330

3 ..290

1.10 Page 10

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APPENDIX E: The Chi-Square Distribution

2 Pages 11-20

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2.1 Page 11

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FORMULA SHEET

= + Me L c[O.Sn-CF]

fme

x-=-

Ifx

Z~(

v~n )

= i-µ

tstat -s-

../n

z _ (n-l)S 2

Xstat - aZ

= b nixy-Ixiy

nix2-(Lx)z

tr=---x1 +x,

nl +n2

x-=-

p±zf!

Z=-

x-µ

= = P(X k) e-00x

I(x·-i)

==-:....,:_I____:_

n-1

= f'

RTXCT