FAS411S - FUNDAMENTALS OF AGRICULTURAL STATISTICS - 2ND OPP - JULY 2024 :: NUST past examination papers between 2020 and 2024

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FAS411S - FUNDAMENTALS OF AGRICULTURAL STATISTICS - 2ND OPP - JULY 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

FAS411S - FUNDAMENTALS OF AGRICULTURAL STATISTICS - 2ND OPP - JULY 2024

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 SCIENCESAND 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: JULY 2024

PAPER:2

DURATION: 3 HOURS

MARKS: 100

SECOND OPPORTUNITY EXAMINATION QUESTION PAPER

EXAMINER(S) Ms. E MATALI

MODERATOR: Mr. M Lubinda (Internal)

INSTRUCTIONS

1. For SECTION A write down the letter corresponding to the best option for each

question

2. For SECTION B show clearly all your work

3. All written work MUST be done 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

[20 marks]

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

1.1. The collection of all possible outcomes is called:

a) Venn diagram

b) Sample space

c) Joint probability

d) Union of events e)

(2)

1.2. A glass jar contains 5 red, 3 blue and 2 green jelly beans. If a jelly bean is chosen at

random from the jar, what is the probability that it is not blue?

a)~

b)2_

c)-7

d) 0.35

(2)

1.3. Which parameter characterizes a Poisson distribution?

a)n

b) p

c) il

d)µ

(2)

1.4. Which of the following sources provides secondary data for research purposes

a) Survey conducted by the researcher

b) Government census reports and databases

c) Data collected from experiments

d) Interviews with industry experts

(2)

1.5. If two events are mutually exclusive and collectively exhaustive, the probability of

their union is equal to

a) O

b) 0.5

c) 1

d) Cannot be determined from the information given

(2)

1.3 Page 3

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1.6. Which statistical measures assessesthe strength of the relationship between two

variables:

a) Standard deviation

b) Mean

c) Mode

d) Correlation coefficient

(2)

1.7. Which of the following distributions is used to model rare events occurring in a fixed

interval of time or space?

a) Poison distribution

b) Binomial distribution

c) Normal distribution

d) Exponential distribution

(2)

1.8. What is the range of values for the number of successes in a binomial distribution?

a) 0 to infinity

b) 1 to infinity

c) Oto n

d) 1 ton

(2)

1.9. Which of the following symbols represents the intersection of sets A and B?

a) U

b)n

c) 0

d) O

(2)

1.10. Which ofthe following factors affects the width of a confidence interval?

a) Population size

b) Sample size

c) Confidence level

d) Standard deviation

(2)

1.4 Page 4

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SECTION B

QUESTION 2

(28 marks]

2.1. Let the Sample Space be the collection of all possible outcomes of rolling one die:

(10]

s {1, 2, 3, 4, 5, 16}

S = {1, 2, 3, 4, 5, 6} A= { 2, 4, 6}

B = {4, 5, 6}

= 2.1.1. An B

{2)

= 2.1.2. Au B

{2)

2.1.3.A UA =

(2)

2.1.4. B =

(2)

2.1.5. A=

{2)

2.2. At NUST all the first-year students who have registered in the school of natural science

are required to take AGSlA and AGS1B. Suppose that 20% of the freshmen fail in AGSlA, 13%

fail in AGS1B and 4% fail both courses.

[5]

2.2.1. Find the probability that a first-year student from the school of natural science picked

at random failed at least one course.

(5)

2.3. Make a stem-and-leaf plot of the set of data below:

121, 90, 83, 97, 96, 84,110,118,128, and 120

[5]

1.5 Page 5

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2.4. You are given the following data below. Calculate the following:

[8]

2.4.1. The mean

(2)

2.4.2. The median

(3)

2.4.3. The standard deviation

(5)

Question 3

3.1. Consider a random variable, X, with the following probability distribution.

[26 marks]

[12]

j 25

~.25

I 0.15

3.1.1. Construct a probability distribution table using the provided data for the random

variable X.

(6)

3.1.2. Calculate the mean (expected value) of X.

(2)

3.1.3. Determine the variance of X.

(2)

3.1.4. Determine the standard deviation of X.

(2)

3.2. A textile producer has established that the spinning machine stops randomly due to

thread breakages at an average rate of 5 stoppages per hour.

[14]

3.2.1. What is the probability that in a given hour 3 stoppages will occur on this spinning

machine?

(2)

3.2.2. What is the probability that in a given hour at most 2 stoppages will occur on this

spinning machine?

(4)

3.2.3. What is the probability that in a given hour more than 4 stoppages will occur on this

spinning machine?

(4)

3.2.4. What is the probability that in 2 hours more than 4 stoppages will occur on this spinning

machine?

(4)

1.6 Page 6

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Question 4

(26 marks]

4.1. Agricultural electronic books (e-books) are becoming a reality thanks to the computer

age. However, agricultural e-books are not cheap as the average price in 2009 was N$400 per

book. Suppose the price of agricultural e-books is normally distributed with a standard

deviation of N$150. What is the percentage of agricultural e-books being sold in 2009 were

priced

(14]

4.1.1. Between N$300 and N$600

(6)

4.1.2. Lessthan N$250

(4)

4.1.3. More than N$250

(4)

4.2. A company manufactures agricultural machinery batteries with an average life span of 2

or more years. An agricultural engineer believes this value to be less Using 10 samples, he

measures the average life span to be 1.8 years with a standard deviation of 0.15. (12]

a) State the null and alternative hypotheses.

(4)

b) At a 99% confidence level, is there enough evidence to discard the null hypothesis?

(8)

END OF PAPER (100]

1.7 Page 7

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FORMULA SHEET

a'r,',f:~.;;.

b = rtl:.o·-txty

tt t..-1-a;.-)1

; = x, +x1

I +ni

a=J-b

1.8 Page 8

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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

.02

.03

.04 .0• 5 .06

.07

.08

.09 -·

.J.4 .0003 .0003 0003 OOJ3 .0003 .0003 .CC03 .0003 .0003 .0002

.3.3

t -3.2

-3.1

.0005 .0005

.OC-07 .0007

.0010 .0009

.0005 .OOJ4 .000-1 - ,0004

.0000 .0006 .0006 .0006

.oons, .0009 .0008 .0008

.0004 .0004

.0006 .0005

.COOS .0008

.OOOt .0003

.0005 0005

.0007 .0007

.3.0 .0013 .0013 .0013 0012 .0012 .0011 .0011

I -2.9 .0019 .001$ 0018 .0017 .0016 .0016 .0015

-2.8

-2.7

-2.6

I I .0026 I .0025

.0035 .0034

I I .00.V .0045

.0024 I .0023 I .0023 I .0022 I .0021

.0033 0032 0031 .0030 .0029

.0044 .0043 ,004'1 .0040 .0039

.0011

.0015

.0021

.0028

0038

.0010

.001..

.0020

0027

.0037

.0010

.001~

.0019

0026

.0036

l -2.5 .0062 .0060 .0059 .0057 .0055 .OOSd .0052 .0051 .OQ.!9 .~8

.2.4 .0082 .0000 0078 .0075 .0073 .0071 .CC69 .0008 .0066 .O~

,2.3 .0107 .0104 0102 0099 .0096 .00~ .0091 .0069 .0087 .0084

-2.2 .013.9 .0136 0132 .0129 .0'125 .0122 .0119 .0116 .0113 .0110

.2.1 .0179 .0174 .Q'170 .0166 .0162

. I -2.0

.1.9

.0228

.0287

.0222

.0281

0217

.0274

-.0212

.0268

.0207

.0262

.0158

.0202

,0256

.0154

.0197

.0250

. .0-150

.0192

.02.U

.01>!6 .0143

.0188 0183

.0:?39 .0233

1 I I .1.8 .0369 .0351 .034il I .0335 .0329 I .0322

I I I .1.7 .~d6 .~36 .0427 .04 8 .OJ09 .OJOI

.031d

.0392

.0307

.0384

.0301

.0375

.02~

.0367

.1.6 .0548 .0537 0526 .0516 .0:-05 .0495 .~85 .0475 .0465 .0455

-1.5 .066e .0656 .0643 06~ .0618 .0606 .0594 .05-82 .Cb71 .0559

-1.4 .oeoe .0793 077$ .0764 .0749 .0735 .0721 .0700 .06..<l! .0681

.1.3 .0966 .0951 ,09}j 09l8 .0001 .0885 .0669 .0853 .0338 0823

-1.2 .1151 .1131 1112 , 1(}93 .1075 .1056 .1038 .1020 .1003 .0985

-1.1

J -1.0

. 1357 .1335 l3U

1292 .1271 .1261-- .1230 .1210 .1190 .1170

.1587 .1562 1539 .1515 .td92 .1469 .1446 .1423 . ldOI .1379

-0.9 .18-!I .1814 1788 .1762 .1735 .1711 .1685 .1660 .1635 .1611

-0.8 .2119 .2090 206'1 1033 .20:>5 .1977 .1~9 .1922 .189-1

I I I I I I --0.7 - .2.420 2389 2358 2327 ..?2% .2266 2236 .2200 .2177

I I I I I .0.6 .27.!3 .2709 2576 ~, 2643 .2611 ,2578 .25J6 .2514 .2A83

.o.s .3085 .3050 .3015 .2981 .2$.16 .2912 .2877 .28A3 .2810

.1667

,21-48

.2451

2TT6

-0.4 .3446 .3409 .3.372 .333-6 .3300 .3264 .3228 .3192 .3156 .3121

-0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483

l• -0.2

I -0.1

0.0

.4207

.4602

.5000

.4168

.4562

.4960

.4129

4522

4920

.4090

4'!83

4880

.4052

.4443

.4e.tO-

.4013

.4404

.4801

.3974

•.t364

..!761

.3936 .3897 .38~

.4325 -.4286 .4247

.4721 .4681 .4641

1.9 Page 9

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Cumulative probabilities for POSITIVEz-values are shown below.

0.0

¥ 0.1

t 0.2

0.3

0.4

0.5

0.6

0.7

0.8

: 0.9

1.0

1.1

1.2

: 1.3

\\ 1.4

1.5

1.6

1.7

j 1.8

1.9

I 2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

! 2.9

3.0

3.1

3.2

3.3

) 3.4

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

.5000 .5040 .5080 .5120 .5160 .519S .5239 .5279 .5319 .535'9

.5398-

.5793

.5438

.5832

.5478

.5371

.5517

.5910

.5557

.5948

.5596

.5987

.f-636

.6026

.5675

.606-i

.5714 ' .5753

.6103 .6141

.6179 .6217 .6255 .6293 .6331 .6368 .6406 .6-!i!J .6400 ,6517

I 1 I I .6~

.6S91 .6628 .6664 .6700 .6736 .G1n .6808 .6844 .6879

I I I I I I I I I I .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224

.7257 7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549

.7580 .761'1 .7642 .7673 .7704 .n34 .n64 .779J .7823 .7852

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

.8159 8186 8212 .82~8 .8264 .8289 .a3l5 .8~0 .8365 .8.38,9

.~13

.ssn .8438 .8461 .8.i85 .85Q8 .8531 .8554

.8599 .8621

.8643 8665 .8-586 .8708 .8729 .8749 .8770 .8790 .8810 .8830

.8849 .8869 .8888 8907 .8925 .8944 .8962 .8980 .8997 .90'15

.9032 .9049 .9066 .9082 .9099 .9115 .9131

I I I l I I I .9192 .':1207 .9222 .9236 .925t .9265 .9279

.9332 .9345 .9357 .9370 .9~92 .9394 .94C~

.9147

.9292

.9418

.9162

.9300

.9J29

.9tn

.9319

.9441

.9.!52 .9J63 .9J74

I I .955d I 9.564 .9573

I .9641 .~.>49 .9656

.9713 9719 .9726

.9J84

.9-582

.%64

.9732

.9495

.959t

.967t

.9738

.9505

.9599

.9678

.9744

.95'15

.$1$08

.9686

.9750

.9525

.9616

JJ693

.9756

.9535

.962:;

.9699

.9761

.9545

.9633

.97~

.9767

.9TT2 9778 97a3 .9788 .9793 .9798 .9803 .9808 .9812 .9817

.9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9354 .9857

.9861 .9864 9858 .9871 .9875 .9878 .9381 .98oi! .9887 .9890

.9893

.9918

.9938

.9S96 .9898

.9920 .9922

.9"';)-10 .9941

.9901

.9925

.9~3

.9904

.9927

.9945

.9906

.9929

.9946

.9"'.109 .9911

.9931 .9932

.9948 .~9

.9913

.9951

.9916

.9936

.9952

.9953

.9965

.9974

.9955

.9966

.~75

.9956

.9967

997G

.9957

.9968

.9977

.S959

.9969

.9977

.9960

.9970

.9978

.9961 .Sf.;62 .9963 .9964

I I I .9971 .9972 .9973 .997J

.9979 .9979 .9980 .9981

.9981 .9982 .9982 .9983 .9984 .998J .9985 .9985 .9986 .9986

.9987

.9990

.9987

.99~fl

.9987

9991

.9988 .9988 .9989 .9989 .9989 .9990 .9990

.9991 .9992 .9992 .9992 .m2 .9993 .%93

.9993 9993 .9994 .9994 .9994 .999-S .9994 .9995 .9995 .9995

.9995 .ms .9995 .9996 .9996 .mG .9996 .9996 .~396 .9997

.9997 .9997 9997 .9997 .9997 .9997 .9997 .~97 .9997 .9998

1.10 Page 10

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TABLE of CRITICAL VALUES for STUDENT'S 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 0256

26 0.256

27 0.256

28 0.256

29 0256

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 0.2tl5

60 0.254

,oo

0.254

120 0.254

140 0.254

, 160 0.25-4

180 0.2S4

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

9,690

0.689

0.688

0.687

0.686

0.685

0.684

0.683

0.682

0.681

0.679

0.678

0.677

0.6n

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

1.3t4

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

1 288

1.285

1.282

0.05 0.04 0.025 0.02 0.01

6.314 7.916 12.706 15.894 31.821

2.920 3.320 4.303 4.849 6.935

2.353 2.605 3.182 3.482 4.541

2.132 2.333 2.776 2_999 3.747

2.015 2.191 2 671 2 757 3.365

1.943 2.104 2_447 2.612 3.143

1.895 2.046 2 365 2.517 2.998

1.860 2.004 2.306 2-449 2.896

1.833 1.973 2.262 2.398 2.821

1.812 1.9-48 2..228 2.359 2.764

1.796 1.928 2.201 2.328 2.718

1.782 1.912 2.179 2.303 2.681

1.771 1.899 2.160 2.282 2.650

1.761 1.887 2.145 2.264 2.624

1.753 1.878 2.131 2.249 2.602.

1.746 1.869 2.120 2.235 2.5&3

1.74-0 1.862 2.110 2.224 2.567

1.734 1.855 2.101 2.21'4 2.552

1.729 1.850 2.()9.3 2.205 2.53.9

1.ns. 1.844 2.086 2.197 .2.528

1.721 1.840 2.080 2.189 2.518

1.717 · 1.83_5 2.074 2,.183 2.508

1.714 l.832 . 2.069 2.1n 2.500

1.711 1.8i8 2.W4 2.172 2.492

1.708 1.825 2.000 2.167 2.485

1.706 1.822 2.056 2.162 2.479

1.703 1.819 2.052 2.158 2.473

1.701 1.817 2.048 2.154 2.467

1.699 1.814 2.045 2.150 2.462

1.697 1.812 2.042 2.147 2.457

1.696 1.810 2.040 '2.144 2.453

1.694 1.808 2.037 2.141 2.449

1.692 1.606 2.035 2.138 2.445

f.691 1.805 2.032 2.136 2.44·1

1.690 1.803 2.030 2:133 2.438

1.688 1.802 2.028 . 2.131 2.434

1.687 1.800 2.026 2.129 2.431

1.686 1.799 2.024 2.127 ' 2A29

1.685 1.700 2.023 2-126 2,426

1.684 J.796 .. 2.02_1 2,123 2 423

1.671 1,781 2.00_0 2..()99 2.390

1.664 1.n3 1.990 2.088 2.374

1.660 1.769 1.984 2.081 2.364

1.658 1.766 t.980 2.076 2358

1.655 1.763 1.977 2073 2.353

1.654 1.762 1.975 2.071 2.350

1.653 1.761 1.973 2.059 2.347

1.653 1.760 1.972 2067 2.345

1,651 1.758 1.969 2.065 2.341

1.645 1.751 1.980 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

2,8_19

2.807

2.797

2.787

2.n9

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

2.607

2.603

2.601

2.596

2.576

0.0025 0.001 0.00,05

127.321 318.289 636.578

14.089 2.2.328 . 31.600

7.453 10.214 12.924

5.598 7.173 8.610

4.773 5.894 6.869

4.317 . 5.208 6.959

4.029 4.786 5.408

3.833 4.501 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

3.252 3.686 4.015

3.222 3.646 3.965

3.197 3.610 3.922

3.174 . 3.579 3.883

3.153 3.552 3.850

3.135 3,627 3.819

3.119 3.505 3.792

_3.104 3.485 3;768.

3.091 3.467 ~.745

3.078 3.450 3.725

3.057 3.435 3.707

3.057 3.421 3.689

3.047 3.408 3.674

3.038 3.396 3.660

3.030 3.385 3.846

3.022 3.375 3.633

3.015 3.365 3.622

3.008 3.356 3.611

3.002 3.348 3.601

2.996 3.340 3.591

2.990 3.333 3.582

2.985 3.326 3.574

2.980 3.319 3.668

2.976 3.313 3.658

2.971 3.307 . 3.651

2.915 ~.232 3.460

2.887 3.195 3.416

2.871 3.174 3.390

2.860 3.160 3.373

2.852 3.149 3.361

2.847 3.142 3.352

2,842 3.138 3.346

2.838 3.131 3,340

2.832 3.123 3.330

2.807 3.090 3,290

2 Pages 11-20

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2.1 Page 11

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A PENo•x E: The hi-Square istribution

~i f .OK-, .t90 i .97:'i .9$t

·*

I .,so

.!,00

.1so

,lto

rm .tiO

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