IAS501S - INTRODUCTION TO APPLIED STATISTICS - 2ND OPP - JULY 2023 :: NUST past examination papers between 2020 and 2024

Expand document

Collapse document

IAS501S - INTRODUCTION TO APPLIED STATISTICS - 2ND OPP - JULY 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

2.2 Page 12

IAS501S - INTRODUCTION TO APPLIED STATISTICS - 2ND OPP - JULY 2023

1 Pages 1-10

▲back to top

1.1 Page 1

▲back to top

nAmlBIA UnlVERSITY

OF SCIEnCE Ano TECHn0L0GY

FACULTYOF HEALTH,NATURALRESOURCESAND APPLIEDSCIENCES

SCHOOLOF NATURALAND APPLIEDSCIENCES

DEPARTMENTOF MATHEMATICS, STATISTICSAND ACTUARIALSCIENCE

QUALIFICATION: Bachelor of Science in Applied Mathematics and Statistics

Bachelor of Tourism Innovation and Development

Bachelor of Natural Resource Management and Nature Conservation

QUALIFICATIONCODE:07BSAM ;

07BTID ; 07BNTC

LEVEL: 5

COURSECODE: IASS0lS

COURSENAME: INTRODUCTION TO APPLIED

STATISTICS

SESSION:

JULY 2023

PAPER:

THEORY

DURATION: 3 HOURS

MARKS:

100

SUPPLEMENTARY/ SECONDOPPORTUNITYEXAMINATION QUESTION PAPER

EXAMINER(S) MR. ROUX, AJ & MR. KASHIHALWA, S

MODERATOR: DR. D. NRIRAMPEBA

INSTRUCTIONS

1. Answer ALL the questions.

PERMISSIBLEMATERIALS

1. Non-Programable Scientific Calculator

ATTACHMENTS

1. Statistical Tables (z-tables)

2. 1 x A4 Graph Paper (to be supplied by Examinations Department)

3. Formulae Sheets

THIS QUESTION PAPERCONSISTSOF 8 PAGES(Including this front page)

1.2 Page 2

▲back to top

QUESTION 1

f 15 X 2 = 30 l

A numerical value used as a summary measure for a sample, such as sample mean, is

known as a

A. population parameter

B. sample parameter

C. sample statistic

D. population mean

E. None of the above answers is correct.

If a data set has an even number of observations, the median

A. can not be determined

B. is the average value of the two middle items

C. must be equal to the mean

D. is the average value of the two middle items when all items are arranged in ascending

order

E. None of the above answers is correct

The standard deviation of a sample of 100 observations equals 64. The variance of the

sample equals

A. 8

B. 10

C. 6400

D.4096

E. None of the above answers is correct.

4. The variance of a sample of 81 observations equals 64. The standard deviation of the

sample equals

A.O

B.4096

C. 8

D. 6,561

E. None of the above answers is correct.

1.3 Page 3

▲back to top

Case 1: Consider the result of a fictional Stats final exam taken by 155 students, as given

in the following relative frequency distribution:

Grade

frequency

Less

than 50

50-59

60- 69 70- 79 80- 89 90-

100

5. Refer to Case 1- How many students received at least a 70 in this exam?

A.25

B.50

C. 25

D.30

E.40

Refer to Case 1- How many students received at most a 59 on this exam?

A.10

B.45

C. 75

D.40

E.66

Case2 : The following data show the number of hours worked by 200 statistics students.

Number of Hours Frequency

HOURS

0 --- 9

10 ---- 19

20 ---- 29

30 ---- 39

# Students

1.4 Page 4

▲back to top

Refer to Case 2. The class width for this distribution

A. 9

B.10

C. 11

D. varies from class to class

E. None of the above answers is correct.

Refer to Case 2. The number of students working 19 hours or less

A. 40

B.50

C. 90

D. can not be determined without the original data

E. None of the above answers is correct.

Refer to Case 2. The relative frequency of students working 9 hours or less

A. 0.2

B. 0.45

C. 40

D. can not be determined from the information given

E. None of the above answers is correct.

10. Refer to Case 2. The cumulative relative frequency for the class of 10 - 19

A.90

B. 0.25

C. 0.45

D. can not be determined from the information given

E. None of the above answers is correct.

1.5 Page 5

▲back to top

11. A teacher asks students to identity their favourite reality television show. What type of

measurement scale do the different television shows make up?

Nominal

B. Ordinal

C. Interval

D. Ratio

12. The seminar rooms in the library are identified by the letters A to H. A researcher

records the number of classes held in each room during the first semester. What kind of graph

would be appropriate to present the frequency distributions of these data?

Histogram

B. Scatterplot

C. Bar chart

D. Box plot

13. What is the mean for the following scores: 2, 5, 4, 1, 8?

B. 4

C. 5

D. 20

14. What is the median for the following scores: 2, 5, 4, 1, 8?

3.5

B. 4

C. 4.5

D. 7

1.6 Page 6

▲back to top

15. Which of the following sets of scores has the greatest variability ( range)?

A. 2, 5, 8, 11

B. 13, 13, 13, 13

C. C.20,25,26,27

D. D.42,43,44,45

QUESTION 2

[15]

The distance traveled (in kilometers) by a courier service motorcycle on 30 trips were

recorded by the driver.

224

219

221

227

220

217

232

222

226

218

213

223

230

210

213

218

222

234

216

218

223 215

219

228

225

220

217

215

2.1) Use the data provided above to construct a frequency distribution table with 210 as the

lower limit of your first class interval and a constant width of four (4) units for all

intervals.

(7)

2.2) Construct a histogram and a polygon of the relative frequency distribution,

(8)

QUESTION 3

[161

A marketing research survey shows that approximately 80% of car owners indicate that

their next car purchase would be an electric propelled car. If 5 prospective buyers are

interviewed, determine the probability that:

3.1) all 5 indicate that their next car will be an electric propelled car.

(4)

3.2) At least three indicate that his or her next purchase will be an electric propelled car.

(4)

3.3) no-one indicates that their next car will be an electric propelled car

(4)

3.4) At most one indicates that his or her next purchase will be an electric propelled car.

(4)

1.7 Page 7

▲back to top

QUESTION 4

[30]

4.1} Pulse rates of adult men are approximately normally distributed with a mean of 70 and

a standard deviation of 8. What is the probability of selecting a man with pulse rate of

4.1.1} 74.9 and higher

(4)

4.1.2} 64.1 and lower

(4)

4.1.3} 82.3 and lower

(4)

4.1.4} What is the probability that the pulse rate for a sample of four men will be between

66.8 and 72.7 (inclusive}

(8}

4.2) Three airlines serve a small town. Airline A has 50% of all the scheduled flights, where-as

airline B has 30% and airline Chas the remaining 20% of all scheduled flights. Their on-

time rates are 80%, 65% and 40% respectively. An airplane has just left.

Let A={airline A}, B={airline B}, C={airline C}, D={airline left on time}

4.2.1} What is the probability that the airplane has left on time?

(6}

4.2.2} If an airplane left on time what is the probability that it belonged to airline A (4)

1.8 Page 8

▲back to top

QUESTION5 [9]

The Tuck-shop on campus has compiled the following information on the prices and quantities

of snacks from 2017 to 2022

ITEM

2017

2022

2017

2022

Toffees

Lollies

Chocolates

1.85

1.50

3.40

3.75

2.25

5.40

110

140

260

250

335

Use 2017 as the base period to determine and interpret the simple price indexes for these

three items in 2022.

(9)

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

1.9 Page 9

▲back to top

STANDARD NORM ALDISTRIBUTION

.00

.01

.02

-3.9 .00005 .00005 .00004

-3.8 .00007 .00007 .00007

-3.7 .00011 .00010 .00010

-3.6 .00016 .00015 .00015

-3.5 .00023 .00022 .00022

-3.4 .00034 .00032 .00031

-3.3 .00048 .00047 .00045

-3.2 .00069 .00066 .00064

-3.I .00097 .00094 .00090

-3.0 .00135 .00131 .00126

-2.9 .00187 .00181 .00175

-2.8 .00256 .00248 .00240

-2.7 .00347 .00336 .00326

-2.6 .00466 .00453 .00440

-2.5 .00621 .00604 .00587

-2.4 .00820 .00798 .00776

-2.3 .01072 .01044 .01017

-2.2 .01390 .01355 .01321

-2.1 .01786 .01743 .01700

-2.0 .02275 .02222 .02169

-1.9 .02872 .02807 .02743

-1.8 .03593 .03515 .03438

-1.7 .04457 .04363 .04272

-1.6 .05480 .05370 .05262

-1.5 .06681 .06552 .06426

-1.4 .08076 .07927 .07780

-1.3 .09680 .09510 .09342

-1.2 .11507 .11314 .11123

-1.l .13567 .13350 .13136

-1.0 .15866 .15625 .15386

-0.9 .18406 .18141 .17879

-0.8 .21186 .20897 .20611

-0.7 .24196 .23885 .23576

-0.6 .27425 .27093 .26763

-0.5 .30854 .30503 .30153

-0.4 .34458 .34090 .33724

-0.3 .38209 .37828 .37448

-0.2 .42074 .41683 .41294

-0.l .46017 .45620 .45224

-0.0 .50000 .49601 .49202

: T able VIa ues Represen t ARE'A t0 the LEFT 0 fth e Z score.

.03

.04

.OS

.06

.07

.08

.09

.00004 .00004 .00004 .00004 .00004 .00003 .00003

.00006 .00006 .00006 .00006 .00005 .00005 .00005

.00010 .00009 .00009 .00008 .00008 .00008 .00008

.00014 .00014 .00013 .00013 .00012 .00012 .00011

.00021 .00020 .00019 .00019 .00018 .00017 .00017

.00030 .00029 .00028 .00027 .00026 .00025 .00024

.00043 .00042 .00040 .00039 .00038 .00036 .00035

.00062 .00060 .00058 .00056 .00054 .00052 .00050

.00087 .00084 .00082 .00079 .00076 .00074 .00071

.00122 .00118 .00114 .00111 .00107 .00104 .00100

.00169 .00164 .00159 .00154 .00149 .00144 .00139

.00233 .00226 .00219 .00212 .00205 .00199 .00193

.00317 .00307 .00298 .00289 .00280 .00272 .00264

.00427 .00415 .00402 .00391 .00379 .00368 .00357

.00570 .00554 .00539 .00523 .00508 .00494 .00480

.00755 .00734 .00714 .00695 .00676 .00657 .00639

.00990 .00964 .00939 .00914 .00889 .00866 .00842

.01287 .01255 .01222 .01191 .01160 .01130 .01101

.01659 .01618 .01578 .01539 .01500 .01463 .01426

.02118 .02068 .02018 .01970 .01923 .01876 .01831

.02680 .02619 .02559 .02500 .02442 .02385 .02330

.03362 .03288 .03216 .03144 .03074 .Q3005 .02938

.04182 .04093 .04006 .03920 .03836 .03754 .03673

.05155 .05050 .04947 .04846 .04746 .04648 .04551

.06301 .06178 .06057 .05938 .05821 .05705 .05592

.07636 .07493 .07353 .07215 .07078 .06944 .06811

.09176 .09012 .08851 .08691 .08534 .08379 .08226

.10935 .10749 .10565 .10383 .10204 .10027 .09853

.12924 .12714 .12507 .12302 .12100 .11900 .11702

.15151 .14917 .14686 .14457 .14231 .14007 .13786

.17619 .17361 .17106 .16853 .16602 .16354 .16109

.20327

.23270

.20045

.22965

.19766

.22663

.19489

.22363

.19215

.22065

.18943

.21770

.18673

.21476

.26435 .26109 .25785 .25463 .25143 .24825 .24510

.29806 .29460 .29116 .28774 .28434 .28096 .27760

.33360

.37070

.40905

.32997

.36693

.40517

.32636

.36317

.40129

.32276

.35942

.39743

.31918

.35569

.39358

.31561

.35197

.38974

.31207

.34827

.38591

.44828

.48803

.44433

.48405

.44038

.48006

.43644

.47608

.43251 .42858

.47210 .46812

.42465

.46414

R·I·T-

www.rit.edu/asc

1.10 Page 10

▲back to top

STANDARD NORMAL DISTRIBUTION : Table VaIues R epresen t AREA tot he LEFT of the Z score.

z .00

.01

.02

.03

.04

.05

.06

.07

.08

.09

0.0 .50000 .50399 .50798 .51197 .51595 .51994 .52392 .52790 .53188 .53586

0.1 .53983 .54380 .54776 .55172 .55567 .55962 .56356 .56749 .57142 .57535

-·--· 0.2 .57926 .58317 .58706 .59095 .59483 .59871 .60257 .60642 .61026 .61409

0.3 .61791 .62172 .62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173

0.4 .65542 .65910 .66276 .66640 .67003 .67364 .67724 .68082 .68439 .68793

0.5 .69146 .69497 .69847 .70194 .70540 .70884 .71226 .71566 .71904 .72240

0.6 .72575 .72907 .73237 .73565 .73891 .74215 .74537 .74857 .75175 .75490

0.7 .75804 .76115 .76424 .76730 .77035 .77337 .77637 .77935 .78230 .78524

0.8 .78814 .79103 .79389 .79673 .79955 .80234 .80511 .80785 .81057 .81327

0.9 .81594 .81859 .82121 .82381 .82639 .82894 .83147 .83398 .83646 .83891

1.0 .84134 .84375 .84614 .84849 .85083 .85314 .85543 .85769 .85993 .86214

1.1 .86433 .86650 .86864 .87076 .87286 .87493 .87698 .87900 .88100 .88298

1.2 .88493 .88686 .88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147

1.3 .90320 .90490 .90658 .90824 .90988 .91149 .91309 .91466 .91621 .91774

1.4 .91924 .92073 .92220 .92364 .92507 .92647 .92785 .92922 .93056 .93189

1.5 .93319 .93448 .93574 .93699 .93822 .93943 .94062 .94179 .94295 .94408

1.6 .94520 .94630 .94738 .94845 .94950 .95053 .95154 .95254 .95352 .95449

1.7 .95543 .95637 .95728 .95818 .95907 .95994 .96080 .96164 .96246 .96327

1.8 .96407 .96485 .96562 .96638 .96712 .96784 .96856 .96926 .96995 .97062

1.9 .97128 .97193 .97257 .97320 .97381 .97441 .97500 .97558 .97615 .97670

2.0 .97725 .97778 .97831 .97882 .97932 .97982 .98030 .98077 .98124 .98169

2.1 .98214 .98257 .98300 .98341 .98382 .98422 .98461 .98500 .98537 .98574

2.2 .-98610 .98645 .98679 .98713 .98745 .98778 .98809 .98840 .98870 .98899

2.3 .98928 .98956 .98983 .99010 .99036 .99061 .99086 .99111 .99134 .99158

2.4 .99180 .99202 .99224 .99245 .99266 .99286 .99305 .99324 .99343 .99361

2.5 .99379 .99396 .99413 .99430 .99446 .99461 .99477 .99492 .99506 .99520

2.6 .99534 .99547 .99560 .99573 .99585 .99598 .99609 .99621 .99632 .99643

2.7 .99653 .99664 .99674 .99683 .99693 .99702 .99711 .99720 .99728 .99736

2.8 .99744 .99752 .99760 .99767 .99774 .99781 .99788 .99795 .99801 .99807

2.9 .99813 .99819 .99825 .99831 .99836 .9984 l .99846 .99851 .99856 .99861

3.0 .99865 .99869 .99874 .99878 .99882 .99886 .99889 .99893 .99896 .99900

3.1 .99903 .99906 .99910 .99913 .99916 .99918 .99921 .99924 .99926 .99929

3.2 .99931 · .99934 .99936 .99938 .99940 .99942 .99944 .99946 .99948 .99950

3.3 .99952 .99953 .99955 .99957 .99958 .99960 .99961 .99962 .99964 .99965

3.4 .99966 .99968 .99969 .99970 .99971 .99972 .99973 .99974 .99975 .99976

3.5 .99977 .99978 .99978 .99979 .99980 .99981 .99981 .99982 .99983 .99983

3.6 .99984 .99985 .99985 .99986 .99986 .99987 .99987 .99988 .99988 .99989

3.7 .99989 .99990 .99990 .99990 .99991 .99991 .99992 .99992 .99992 .99992

3.8 .99993 .99993 .99993 .99994 .99994 .99994 .99994 .99995 .99995 .99995

3.9 .99995 .99995 .99996 .99996 .99996 .99996 .99996 .99996 .99997 .99997

2 Pages 11-20

▲back to top

2.1 Page 11

▲back to top

Population mean, raw data

Sample mean, raw data

Weighted mean

Geometric mean

Geometric

mean rate of increase

Value at end of period

Value at start of period

- 1.0

Sample mean grouped data

x l;fx

Median of grouped data

Median=

L+

-2"- -CF

Mean deviation

MD = .6 X-X

(Class

width)

Linear regression

equation

Y = a+ hX

Sample

variance

s2 =

for raw data

I: 2

(X- X)

n-1

Sample variance,

raw data

EX2 - (Z:X)'

52 =

n-1

computational

form

Sample standard deviation,

raw data

s=\\

n-1

Sample standard deviation,

grouped data

I l; fX2

(z'.fX)

S = '\\

n- 1

Coefficient

of variation

CV=

(100)

Location

of percentile

Lp = (n + 1)

100

Pearson'

s Correlation

coefficient

n (l:XY) - {l;X) (l:Y)

Correlation

test of hypothesis

Population

standard deviation

for raw data

Population

variance for raw data

02 = .6 ( X -

Slope

of regression

line

n (l;XY) - (I;X)

(E Y)

Intercept

of a regression

line

The Range

Range

highest - lowest

2.2 Page 12

▲back to top

.. '

APPENDIX B: ADDITIONAL FORMULAE

pos1. t.10n

pos1. t.10n½=-jn

100

P(AIB)= P(AnB)

P(B)

z=--x-µ

X1 -X2

-S+1 -- S?

nl n2

value

p = L + .(.._,_j!_!_1_0-_F_0_))_x.:c__

P(x)= n! .1r'(l-Jr)"-x

x!(n-x)!

x-µ

= zca/c

CTI

x-µ

= tca1c

q = 1- p

P= A

(1 + i)"

PV = P(l + i)"

(1+ j)"

r = (l + i) -1 111

D = B(l-i)"