AGS520S - AGRICULTURAL STATISTICS - 2ND OPP - JANUARY 2024 :: NUST past examination papers between 2020 and 2024

Expand document

Collapse document

AGS520S - AGRICULTURAL STATISTICS - 2ND OPP - JANUARY 2024

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

2.3 Page 13

AGS520S - AGRICULTURAL STATISTICS - 2ND OPP - JANUARY 2024

1 Pages 1-10

▲back to top

1.1 Page 1

▲back to top

nAmlBIA UnlVERSITY

OF SCIEnce AnOTECHnOLOGY

FacultyofHealthN, atural

ResourceasndApplied

Sciences

Schoolof NaturalandApplied

Sciences

Departmenot fMathematics.

StatisticsandActuariaSl cience

13JacksonKaujeuaStreet

Private Bag13388

Windhoek

NAMIBIA

T: •264 61207291l

E: msas@nust.na

W: www.nust.n.i

QUALIFICATION : BACHELOR OF AGRICULTURAL MANAGEMENT

QUALIFICATION CODE: 07BAGR

LEVEL: 5

COURSE: AGRICULTURAL STATISTICS

COURSE CODE: AGSS20S

DATE: JANUARY 2024

SESSION: 1

DURATION: 3 HOURS

MARKS: 100

SECOND OPPORTUNITY/ SUPPLEMENTARY: EXAMINATION QUESTION PAPER

EXAMINER:

MODERATOR:

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 8 pages including this front page

1.2 Page 2

▲back to top

SECTION A

QUESTION 1

(24 marks]

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

1.1 Variability is a common characteristic in Biology. A characteristic that varies from

observation to observation in the same group is called.

[2]

mean

B. median

C. Random variable

D. variance

1.2 The branch of statistics devoted to the summarization and description of data is

called:

[2]

Descriptive statistics

B. Inferential statistics

Population statistics

D. Sample statistics

1.3 _____

consist of methods for drawing and measuring the reliability of

conclusions about population based on information obtained from a sample of the

population.

[2]

Probability statistics

B. Descriptive statistics

C. Inferential statistics

D. Sample statistics

Agricultural Statistics (AGS520S)

2nd Opportunity- January 2024

1.3 Page 3

▲back to top

1.4 _______

can be broadly defined as a systematic enquiry into a subject to

discover new facts

[2]

A. Statistics

Research

C. Probability distribution

D. Statistical tables

1.5 Quantitative variables can be classified as:

[2]

Discrete or continuous

Nominal or interval

C. Normal distribution or nominal

D. Ordinal or ratio

1.6 The following are all examples of qualitative data except:

[2]

A. Soil type

8. Type of season

C. Age in years of ten employees

D. Crop variety

1.7 Which of the following is a property of the median?

[2]

Can be distorted by outliers

Cannot be affected by outliers

C. third quartile

D. There may be several medians in the same data set

Agricultural Statistics (AGS520S)

2nd Opportunity- January 2024

1.4 Page 4

▲back to top

1.8 The following are all examples of ordinal scales of measurement except:

[2]

A. Organizational structure

B. Position in the work environment

C. Rank in police force

D. PH scales

1.9 The narrower the confidence interval,

[2]

A. the more precise it is

B. the less precise it is

C. the easier computations

D. the larger the population.

1.10 A random sample of eight observations from a population containing 58 elements

was taken, and the following values were obtained. The sample mean is:

(2)

12, 16,19,21,24,25,17,32

A. 19.25

B. 3.77

C. 8

D. 20.75

1.11 Researchers draw sample because of all the following reasons except

(2)

A. Reduce cost

B. Can be done in a shorter time frame

C. Sampling is interesting

D. Reduction of biases

Agricultural Statistics (AGS520S)

2nd Opportunity- January 2024

1.5 Page 5

▲back to top

1.12 If

H0 : There is no association between variables and H1 : There is an association between variables

,the decision rule for this hypothesis testing is:

[2]

A. reject Ho if xltat x;rit

B. reject Ho if xltat $ x;rit

C. reject Ho if x;rit xlcat

D. reject HO .If Xc2rit -- Xs2tat

SECTION B (Clearly show all your work)

QUESTION 2

(41 marks)

2.1 The following relates to the weights of 36 female students in a state university. The

data were recorded to the nearest pound.

138 146 168 146 161 164 158 126 173

150 140 138 142 135 132 147 176 147

144 136 163 135 150 125 148 120 153

149 152 154 140 145 157 144 165 135

2.1.1 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.

[7]

2.2 Yogurt is one of the best sources of calcium, providing up to 34% of the DV in one

cup. The following table present the distribution of calcium in grams that was

measured from 29 small cups of Yogurt.

Protein contents

(in grams)

0-<10

10-<20

20-<30

30-<40

40-<50

Frequency

Agricultural Statistics (AGS520S)

2nd Opportunity- January 2024

1.6 Page 6

▲back to top

2.2.1 Estimate the average calcium for the Yogurt

[3]

2.2.2 Estimate the median calcium for the Yogurt

[3]

2.2.3 Estimate the mode of calcium for the Yogurt

[3]

2.2.4 Estimate the variance and the standard deviation of calcium for the Yogurt

[6]

2.3

I~(X) I ~-13 I ~.31 I ~.28 I ~.06 I ~.10 I~.12

The random variable X represents the number of milk bottles purchased and P{X)

represent the probability that a customer will buy X bottles of milk.

2.3.1 Calculate the mean number of milk bottles purchased by a customer per

week

[3]

2.3.2 Calculate the variance for the number of milk bottles the customer purchased

[4]

2.3.3 What is the probability that at least five bottles of milk were purchased [2]

2.4 A statistics instructor tracks the calls and texts that he receives on his cell

phone over a month. His results are as follows.

Contact Source

FamilyMember Opinion Survey ScamArtist

Wrong Number

Type of

message

Phone call

Message

Total

2.4.1

2.4.2

2.4.3

What is the probability that the instructor will receive a message from a

family member?

[2]

What is the probability that the instructor received a message or a phone

call?

[2]

What is the probability that the instructor will received a message given that

it was from a Scam Artist?

[3]

Agricultural Statistics (AGS520S)

2nd Opportunity-January 2024

1.7 Page 7

▲back to top

2.4.4 Are the events Phone call and Wrong number independent?

[3]

QUESTION 3

(28 marks)

3.1 It is assumed that a sampling error of no more than ±0.03 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 You sample 36 apples from your farm's harvest of over 200 000 apples. The mean

weight of the population is 112 grams (with a 40-gram population standard deviation).

What is the probability that the sample mean weight of the apples is less than 120

grams?

[3]

3.3 During December 2019, rainfall figures were recorded over 9 farms in the Kunene

region.

Farm

A BC D E F G H I

Rain fall (mm) 35 21 33 24 30 36 27 39 25

3.3.1 At the 10% level of significance test the hypothesis that the average rainfall in Kunene

was above 25 mm.

[8]

3.3.2 Construct a 90% confidence interval to estimate the mean rainfall amount for the

Kunene region.

[6]

3.3.3 What assumption must be made to be sure that the confidence interval in (3.3.2)

above is valid?

[2]

3.4 The variance for the heights (in m 2 ) of a random sample of 10 paw paw trees was

found to be 0.36 m when grown in a natural environment.

3.4.1 Estimate the variance of the entire population of paw paw trees with a 90% degree

of confidence.

[6]

Agricultural Statistics (AGS520S)

2nd Opportunity- January 2024

1.8 Page 8

▲back to top

QUESTION 4

(7 marks)

4.1 A food services manager for a baseball park wants to know if there is a relationship

between gender (male or female) and the preferred condiment on a hot dog. The

following table summarizes the results.

Gender

Condiment

Ketchup Mustard Relish

Male

Female

Total

100

Test the hypothesis to determine if there is a relationship between gender and

condiment on a hot dog using a significance level of 10%.

[7]

*********************END OF EXAMINATIONQUESTIONPAPER********************

Agricultural Statistics (AGS520S)

2nd Opportunity- January 2024

1.9 Page 9

▲back to top

Z-Table

The table shows cumulativeprobabilitiesfor the standardnormal curve.

Cumulativeprobabilitiesfor NEGATIVEz-valuesare shownfirst.SCROLL

DOWNto the 2nd pagefor POSITIVEz

.00

.01

.02

.03 ' .04

-3.4 .0003 .0003 .0003 .0003 I .0003

-3.3 .0005 .0005 .0005 .0004 .0004

I -3.2 .0007 .0007 .0006 .0006 .0006

-3.1 .0010 .0009 .0009

I I -3.0 .0013 .0013 I .0013

-2.9 .0019 .0018 .0018

.0009

.00·12

.0017

.0008

.0012

.0016

-2.8 .0026 .0025 .0024 .0023 .0023

-2.7 .0035 .0034 .0033 .0032 I .0031

-2.6 .0047 .0045 .0044 .0043 .0041

-2.5 .0062 .0060 .0059 .0057 .0055

-2.4 .0082 .0080 .0078 .0075 .0073

-2.3 .0107 .0104 .0102 I .0099 .0096

-2.2 .0139 .0136 .0132 .0129 .0125

-2.1 .0179 .0174 .0170 .0166 .0162

-2.0 .0228 .0222 .0217 .0212 .0207

-1.9 .0287 .0281 .0274 .0268 .0262

-1.8 .0359 .0351 .0344 .0336 .0329

-1.7 .0446 .0436 .0427 .0418 .0409

-1.6 .05<18 .0537 .0526 .0516 .0505

-1.5 .0668 .0655 .0643 .06.30 .0618

-1.4 .0808 .0793 .0778 .0764 .0749

-1.3 .0968 .0951 .0934 .0918 .0901

-1.2 .1151 .1'131 .1112 .1093 .1075

-1.1 .1357 .1335 .1314 .1292 .1271

-1.0 .1587 .1562 .1539 .1515 .1492

-0.9 .1841 .18'14 .1788 .'1762 .1736

1, -0.8 .2119 .2090 .2061 2033 .2005

-0.7 .2420 .2389 .235-S .2327 I .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 .4129 .4090 .4052

-0.1 ,.4602 .4562 .4522 .4483 .4443

0.0 .5000 .4960 .4920 .4880 .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

.171'1

.1977

.2266

.2578

.2912

.3264

.3632

.4013

.4404

.480'1

.06

.0003

.0004

.0006

.0008

.0011

.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

.02.:!4

.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

.1894

.2177

.2483

.2810

.3156

.3520

.3897

.4286

.4681

.09

.0002

.0003

.0005

.0007

.00'IO

.00'14

.0019

.0026

.0036

.0048

.0064

.0084

.D'l'IO

.0143

.0183

.0233

.0294

.0367

.0455

.0559

.0681

.0823

.0985

.1170

.1379

.1611

.1867

.2148

.2451

.2776

.3121

.3483

.3859

.4247

.4641

1.10 Page 10

▲back to top

Cumulative probabilities for POSITIVE z-values are shown below.

0.0

0.1

0.2

I 0.3

0.4

0.5

0.6

I 0.7

0.8

0.9

I 1.0

I 1.1

I 1.2

! 1.3

1.4

' 1.5

I 1.6

! 1.7

I 1.8

1.9

2.0

2.1

2.2

I 2.3

I 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

.964·1

.9713

.9772

.9821

.9861

.9893

.9918

.9938

.9953

.9965

.9974

.9981

.9987

.9990

..9993

.9995

.9997

.01

.5040

.5438

.5832

.6217

.6591

.6950

.7291

.7611

.7910

.8186

.8438

.8665

.8869

.9049

.9207

.9345

.9463

.9564

.9649

.9719

.9778

.9826

.9864

.9896

.9920

.9<J40

.9955

.9966

.9975

.9982

.9987

.999'1

.9993

.9995

.9997

.02

.5080

.5478

.5871

.6255

.6628

.6985

.7324

.7642

.7939

.8212

.8461

.8686

.8888

.9066

.9222

.9357

.9474

.9573

.9656

.9726

.9783

.9830

.9. 868

.9898

.9922 '

.9941

.9956

.9967

.9976

.9982

.9987

.9991

.9994

.9995

.9997

.03

.5120

.5517

.5910

.6293

.6664

.7019

.7357

.7673

.7967

.8238

.8485

.8708

.8907

.9082

.9236

.9370

.9484

.9582

.9654

.9732

.9788

.9834

.9871

.9901

.9925

.9943

.9957

.9968

.9977

.9983

.9988

.999·1

.9994

.9996

.9997

.04

.5160

.. 5557

.5948

.6331

.6700

.7054

.7389

.7704

.7995

.8264

.8508

.8729

.8925

.9099

.9251

.9382

.9495

.9591

.9671

.9738

.9793

.9838

.9875

.9904

.9927

.9945

.S959

.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

.95S9

.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

.9686

.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

.5319

.5714

.6103

.6480

.6844

.7190

.7517

.7823

.8106

.8365

.8599

.8810

.8997

.9162

.9306

.9429

.9535

.9625

.9699

.9761

.9812

.9854

.9887

.9913

.9934

.9951

.9963

.9973

.9980

.9986

.9990

.9993

.9995

.9996

.9997

.09

.5359

.5753

.6141

.6517

.6879

.7224

.7549

.7852

.8133

.8389

.8621

.8830

.9015

.9'177

.9319

.9441

.9545

.9633

.9706

.9767

.9817

.9857

.9890

.9916

.9936

.9952

.9964

.9974

.9981

.9986

.9990

.9993

.9995

.9997

.9998

2 Pages 11-20

▲back to top

2.1 Page 11

▲back to top

TABLE of CRITICAL VALUES for STUDENTS t DISTRIBUTIONS

Column headings denote probabilities (a) above tabulated values.

d.f. 0.40 0.25

1 0.325 1.000

2 0.289 0.816

3 0.277 0.765

4 0.271 0.741

5 0.267 0.727

6 0.265 0.718

7 0.263 0.711

8 0.262 0.706

9 0.261 0.703

10 0.260 0.700

11 0.260 0.697

12 0.259 0.695

13 0.259 0.694

14 0.258 0.692

15 0.258 0.691

16 0.258 0.690

17 0.257 0.689

18 0.257 0.688

19 0.257 0.688

20 0.257 0.687

21 0.257 0.686

22 0.256 0.686

23 0.256 0.685

24 0.256 0.685

25 0.256 0.684

26 0.256 0.684

27 0.256 0.684

28 0.256 0.683

29 0.256 0.683

30 0.256 0.683

31 0.256· 0.682

32 0.255 0.682

33 0.255 0.682

34 0.255 0.682

35 0.255 0.682

36 0.255 0.681

37 0.255 0.681

38 0.255 0.681

39 0.255 0.681

40 0.255 0.681

60 0.254 0.679

80 0.254 0.678

100 0.254 0.677

120 0.254 0.677

140 0.254 0.676

160 0254 0.676

180 0.254 0.676

200 0.254 0.676

250 0.254 0.675

inf 0.253 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 4297 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 3252 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 3232 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

2.2 Page 12

▲back to top

APPENDIX E: The Chi-Square Distribution

I.__-·-·-

2.3 Page 13

▲back to top

FORMULASHEET

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

fme

x- =-

"i,fx

Z~(

v~n )

tstat = -i-,µ-.

-.Jn

2 _ (n-l)S 2

Xstat - qZ

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

n"E,x2-("i,x) 2

1!=---

+x,

nl +n2

x-=-

r,x

p±zf!

P(X = k) = e-eex

= Mo L + c[fm-fm-1]

Z=-a-i-µ

2fm-fm-1-fm+1

(P1 - P2) ± Z~( P1q1 + pzqz)

z n1

< < (n-l)S 2 (Jz

(n-l)S 2

x2za•n-1

x2 1-za,n-1

Xs2tat

Cfo-fe)2

L, fe

=-"-f:',-(nx-·1-i)Z

= S 2

"i,(x·-i)Z f·

n-1

= F RTXCT