IAS501S - INTRODUCTION TO APPLIED STATISTICS - 2NS OPP - JANUARY 2025 :: NUST past examination papers between 2021 and 2025

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IAS501S - INTRODUCTION TO APPLIED STATISTICS - 2NS OPP - JANUARY 2025

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IAS501S - INTRODUCTION TO APPLIED STATISTICS - 2NS OPP - JANUARY 2025

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nAmIBIA unIVERsITV

OF SCIEnCEAno TECHnOLOGY

FacultoyfHealthN, atural

ResourcaensdApplied

Sciences

Schoool f NaturalandApplied

Sciences

Departmentof Mathematics,

StatisticsandActuarialScience

13JacksonKaujeuaStreet

PrivateBag13388

Windhoek

NAMIBIA

T: +264612072913

E: msas@nust.na

W: www.nust.na

QUALIFICATION: BACHELORof SCIENCEIN APPLIEDMATHEMATICS AND STATISTICS&

BACHELORof SCIENCE

QUALIFICATIONCODE: 07BSAM & 07BSOC

LEVEL:5

COURSE:INTRODUCTION TO APPLIEDSTATISTICS

COURSECODE: IASS0lS

DATE: JANUARY2025

SESSION: 1

DURATION: 3 HOURS

MARKS: 100

EXAMINER:

MODERATOR:

SECONDOPPORTUNITY:EXAMINATION QUESTIONPAPER

MR. ANDREW ROUX

DR. DISMAS NTIRAMPEBA

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.

PERMISSIBLEMATERIALS:

1. Non-Programmable Calculator

ATTACHEMENTS

1. Statistical Formulae Sheet

2. Standard Normal Probability Distribution Table

3. 1 x A4 Graph Sheet

This paper consists of 6 pages including this front page

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QUESTION 1

[10x2 = 20]

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

number

1.1. Any characteristic of a population distribution may properly be referred to as a

a.) standard deviation.

b.) standard score.

c.) raw score.

d.) standard error.

e.) parameter.

1.2. Characteristics of a population are called ____ , while those of a sample

are termed ----

a.) statistics; measures

d.) statistics; parameters

b.) parameters; statistics e.) none of these

c.) statistics; variables

1.3. A population is:

a.) a number or measurement collected as a result of observation

b.) a subset of a population

c.) a characteristic of a population which is measurable

d.) a complete set of individuals, objects, or measurements having

some common observable characteristics

e.) none of these

1.4 Your statistics class

a.) is a representative sample of your college student body

b.) is not a representative sample of your college student body

c.) is not a sample of your college student body

d.) none of the above

1.5. Inferential statistics

a.) refers to the process of drawing inferences about the sample based on the

characteristics of the population

b.) is the same as descriptive statistics

c.) refers to the statistical methods used to draw inferences about a

population based

on sample information

d.) is the same as a census

e.) none of the above answers is correct.

1.6. Which of the following is NOT a valid reason for selecting a sample instead

of studying the whole population?

a.) The cost of studying an entire population may be too high.

b.) The population may be at least partially destroyed in the process

of studying it.

c.) Studying the entire population might be too time consuming.

d.) It is very interesting to conduct sampling.

Course Name (Course Code)

rt opportunity November 2023

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1.7. Suppose we sample by selecting every fifth invoice in a file after

randomly obtaining a starting point. What type of sampling is this?

a.) simple random sampling

b.) cluster random sampling

c.) stratified random sampling

d.) systematic random sampling

e.) None of the above

1.8. The ___

sampling method typically will require a larger sample size

than other methods; however, the close proximity of sample elements can

be cost-effective.

a.) simple random

b.) cluster

c.) stratified

d.) systematic

e.) None of the above.

1.9. All possible samples of size n are selected from a population, and the mean

of each sample is determined. The mean of the sample means is ___ _

a.) Exactly the same as the population mean

b.) Larger than the population mean

c.) Smaller than the population mean

d.) Cannot be estimated in advance

e.) None of the above

1.10. The _____

tells us that the distribution of all possible sample means

will be approximately normal for reasonably large sample sizes.

a.) Central Limit Theorem

b.) Mean Limit Theorem

c.) Combination Theorem

d.) Estimation Theorem

e.) None of the above is correct.

QUESTION 2

(18]

The data below represents the annual rainfall (mm) recorded over forty farms across

Namibia in 2018,

250 600 553 295 210 389 400 625 850 723

157 423 300 239 487 535 762 532 672 678

522 435 628 456 239 863 764 433 677 245

342 296 456 586 349 421 568 825 924 598

2.1) Summarize the data in a frequency distribution with classes of equal width

of 100 rand, starting at 100 - < 200 ; 200 - < 300 ; ext..

(4)

Course Name (Course Code)

1st opportunity November 2023

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2.2) Compile a relative frequency distribution distribution

(2)

2.3) Compile a Relative Cumulative "less-tan" and a Relative Cumulative "more-

than frequency distribution

(2 + 2)

2.4) Use the data obtained in 2.1 to draw a histogram and a polygon ( 5 + 3 = 8)

QUESTION 3 [19]

During one month, time records shows the following results for the number of

production workers absent per day:

17 21

For the distribution above, calculate and interpret the:

3.1) Range

(2)

3.2) Mode

(1)

3.3) Median

(3)

3.4) Arithmetic mean

(3)

3.5) Variance

(5)

3.6) Standard deviation

(2)

3.7) Coefficient of variation

(3)

QUESTION 4 [15]

The Office of The Bursar at The Namibia University of Science and Technology

(NUST) revealed some information regarding method of payment for a group of 2022

students at different levels of study.

Bursary Loan Self Totals

Certificate 12

379 727 1118

Diploma 39

106 642 787

Degree 48

20 57 95

Totals

505 1426 2000

4.1) Find the probability of randomly selecting one student from this group who

pays for him/herself?

(2)

Course Name (Course Code)

1st opportunity November 2023

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4.2) Find the probability of randomly selecting one student from this group who

has a Diploma or a Degree?

(4)

4.3) Find the probability of randomly selecting one student from this group who

has a Bursary or Degree?

(4)

4.4) What is the chance of randomly selecting one student with a degree, given

that this student has a loan?

(5)

QUESTION 5

[28]

5.1) In a multiple choice question, there are five different answers, of which only

one is correct. The probability that a student will know the correct answer is

0.6. If a student does not know the answer, he guesses an answer at random.

5.1.1) What is the probability that the student gives the correct answer?

(4)

5.1.2) If the student gives the correct answer, what is the probability that he

guessed?

(6)

5.2) A company's sales for the years 2014 to 2022 were as follows: ( x N$ 10 000 )

2014 2015 2016 2017 2018 2019 2020 2021 2022

324 296 310 305 295 347 348 364 370

5,2.1) Plot the time series data

(4)

5.2.2) Derive, by using the method of least squares, an equation of linear trend for

the sales of the company. (Use sequential numbering with x = 1 in 2012) (8)

5.2.3) Compute trend values for the years 2012 and 2025

(6)

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Course Name (Course Code)

1st opportunity November 2023

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FORMULAESHEET

= + Mean X r.xt · Mode=L

c(fm-fm-i)

2Xfm-fm-1-fm+1

l3= n(L,xy)-(L,x)(L,y)

n(r,x 2 )-(r,x) 2

Med i.an=l + c(O.Sn-CF)

fme

Ip(L) "LPJxO' b ~ x 100

I:Pb X Qb

LP1 Ip =~xl00%

LJP0

Var(x) = LX2 - n(~)2

n-l

CV= Std Dev x 100

; Std Dev, s = -Jvar(x)

Course Name (Course Code)

151Opportunity November 2023

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Z -Table

The table shows cumulativeprobabilitiesfor the standard normal curve.

Cumulative probabilities for NEGATIVE z-values are shown first. SCROLL

DOWNto the 2nd page for POSITIVEz

j -3.4

.00

.0003

-3.3 .0005

I -3.2

.3.1

_-3.0

.0007

.0010

.00·13

l -2.9 .0019

-2.8 .0026

I --2.7 .0035

j,__-2.6 __,0047

l -2.5

-2.4

.0062

.0082

, -2.3 .0107

? -2.2 .0·139

-2.1 .0179

I --2.0

!_ -1.9

.0228

.0287

I -1.8

! -1.7

i -1.6

I -1. .5-- -

I -1.4

.0359

.0446

.0548

.0668

.0808

-1.3 .0968

I -1.2 .1151

i -1.1 .1357

' -1.0 .1587

I .0.9 - .184"1

I .0.8 .2119

I .0.7 .2420

-0.6 .. .2743

.0.5 .3085

.0.4 .3446

.0.3 .3821

.0.2 .4207

! -0.1 .4602

0.0

.5000

.01

.02

.03

.0003 .0003 .0003

.0005 .0005 .0004

.0007 .0006 .0006

.0009 .0009 .0009

.0013 .00'13 . .00·12

.0018 .00'18 .00'17

.0025 .0024 .0023

.0034 .0033 .0032

.004?

:0044

.0. 0.43

.0060 .0059 .0057

.0080 .0078 .0075

.0104 .0102 .0099

.0136 .0132 .0129

.0174 .0170 .0166

.0222 .02'17 .02·12

.0281

.035'1

.0436

.0.2. 74

.0344

.0427

.0268

.0336 .

.04'18

.0537 .0526 .05"16

.0655 .0643 .0630

.0793 .0778 .0764

.095'1 .0934 .0918

.ll31 ."11'12 .'1093

.'1335 .'13'14 .'1292

.'1562 .'1539 .'15'15

.'18'14 .'1788 .'1762

.2090 .2061 .2033

.2389 .2358 .2327

.2709 .. .2676 .2643

.3050 _30·15 .2981

.3409 .3372 .3336

.3783 .3745 .3707

.4168 .4129 .4090

.4562 .4522 .4483

.4960 .4920 .4880

.04

.0003

.0004

.0006

. .0008

.00'12

.0-0.16

.0023

.003·1

.004'1

.0055

.0073

.0096

.0125

.0162

.0207

.0262

.0329 -

.0409

.0505

.0618

.0749

.090'1

.1075

.1271

.1492

.1736

.2005

2296

.2611

.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

.06.!)6

.0735

.0885

.1056

.1251

.1469

.1711

.1977

.2266

.2578

.2912

.3264

.3632

.40'13

.4404

.4801

.06

.07

.08

.0003 .0003 .0003

.0004 .0004 .0004

.0006 .0005 .0005

.0008 .0008 -.0007

.0011 .00'11 .OO'IO

.0015 .00·15 .00·14

.0021 .0021 .0020

.0029 .0028 .0027

_p.93~ .0038 .0.03. 7.

.0052 .0051 .0049

.0069 .0068 .0066

.0091 .0089 .0087

.0119 .01'16 .0113

.0154 .0150 .0146

.0·197 .0192 .0'188

.0250 .. .0244 .. .0239

.0314 .0307 .0301

.0392 .0384 .0375

.0485 .0475 .0465

.0594

.0721

.0582 .. . .0,.571 ..

.0708 .0694

.0869 .0853 .0838

.1038 .1020 .'1003

.1230 .1210 .1190

.'1446 .'1423 .1401

.1685 .'1660 .'1635

.1949 .1922 .1894

.2236 .2206 .211z

.2546 .2514 .2483

.2877 .2843 .2810

.3228 .3192 .3156

.3594 .3557 .3520

.3974 .3936 .3897

.4364 .4325 .4286

.4761 .4721 .4681

.09

.0002

.0003

.0005

.0007

.0010

.00·14

.0019

.0026

-9036

.0048

.0064

.0084

.01'10

.0143

.0183

.0233

.0294

.0367

.0455

.0559,.,

.0681

.0823

.0985

.'1170

.1379

.'16'1"1

.1867

.2148

.2451

.2776

.3121

.3483

.3859

.4247

.4641

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Cumulativeprobabilitiesfor POSITIVEz-valuesare shown below.

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

0.0

.5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359

1 0.1

I 0.2

i 0.3

! 0.4

'I 0.5

I 0...6- -

0.7

.5398

.5793

.6179

.6554

.6915

.7257

.7580

.5438

.5832

.6217

.6591

. .6950

.7291

.7611

.5478

.587"1

.6255

.6§28

.6985

.7324 ..

.7642

.55'17

.59'10

.6293

.6664

.7019

.7357

.7673

.5557

.5948

.6331

.6700

.7054

.7389

.7704

.5596

.5987

.6368

.6736

.7088

.7422

·•

.7734

.5636

.6026

.6406

.6772

.7123

.7454

.7764

.5675 .5714

.6064 .6103

.6443 .6480

.6808 .6844

.7157 .7190

.7486 . - - .7517

.7794 .7823

.5753

.6141

.6517

.6879

.7224

--.7549

.7852

I 0.8

0.9

.7881

.8'159

.7910

.8'186

.7939 .7967

.82'12 .8238

.7995

.8264

.8023

.8289

.8051

.8315

.8078

.8340

.8106

.8365

.8133

.8389

,I 1.0

1.1

1.2

.8413

.8643

.8849

.8438

.8665

.8869

.8461

.8686

.8888

.8485

.8708

.8907

.8508

.8729

.8925

.8531

.8749

.8944

.8554

.8770

.8962

.8577

.8790

.8980

.8599

.8810

.8997

.862'1

.8830

.9015

I 1.3

r 1.4

.9032

.9192

.9049

.9207

.9066

.9222

.9082

.9236

.9099

.9251

.9115

.9265

.9131

.9279

.9147

.9292

.9162

.9306

.9177

.9319

I 1.5

" 1.6

.i 1.7

1.8

1.9

.9332

.9452

.9554

.. .9641

.9713

.9345

.94-6- 3.

.9564

.9649

.9719

.9357

.9474

.9573

.9656

.9726

.9370 .9382 .9394

.9484_ J .9495 : .950..5

.9582 .9591 .9599

.9664 I .9671 .9678

.9732 .9738 .9744

.9406

.9515

.9608

.9686

.9750

.9418

.9525-

.9616

.9693

.9756

.9429

. .-9535

.9625

.9699

.9761

.9441

.9545

.9633

.9706

.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 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890

2.3

.9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 _99·16

l 2.4

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

I 2.5 ... .9938

.9940

.994--1-

.9943

.9945

.9946

.9948

.9949

.9951 . .99..5. 2

2.6

.9953 .9955 .9956 I .9957 .9959 .9960 .9961 .9962 .9963 .9964

I I I :I :I I I I I I 2.7

.9965 _.9966 _:9967 _.9968_ .9%9 .9970 .9971 .9972 .9973 .9974

i 2.8

.9974 .9975 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .998·1

2--.9

.998'1 .9982 .9982 .9983 I .9984 .9984 .9985 .9985 .9986 .9986

3.0

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

; 3.1

.9990 .9991 .9991 _999·1 .9992 .9992 .9992 .9992 .9993 .9993

3.2

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

3.3

.9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .9997

3.4

.9997 .9997 .9997 .9997 .9997 ' .9997 .9997 .9997 .9997 .9998

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