SFE611S - STATISTICS FOR ECONOMISTS - 2ND OPP - JULY 2022 :: NUST past examination papers between 2020 and 2024

Expand document

Collapse document

SFE611S - STATISTICS FOR ECONOMISTS - 2ND OPP - JULY 2022

1 Page 1

2 Page 2

3 Page 3

4 Page 4

5 Page 5

6 Page 6

7 Page 7

8 Page 8

9 Page 9

10 Page 10

SFE611S - STATISTICS FOR ECONOMISTS - 2ND OPP - JULY 2022

1 Page 1

▲back to top

:p i

FACULTY

NAMIBIA UNIVERSITY

OF SCIENCE AND TECHNOLOGY

OF HEALTH, APPLIED SCIENCES AND NATURAL

DEPARTMENT OF MATHEMATICS AND STATISTICS

RESOURCES

QUALIFICATION: BACHELOR OF ECONOMICS

QUALIFICATION CODE: 07BECO

COURSE CODE: SFE611S

LEVEL: 5

COURSE NAME: STATISTICS FOR ECONOMIST

SESSION: JULY 2022

DURATION: 3 Hrs

PAPER: THEORY

MARKS: 100

SECOND OPPORTUNITY/SUPPLEMENTARY EXAMINATION QUESTION PAPER

EXAMINER

Mr J. Amunyela

MODERATOR:

Mr A.Roux

INSTRUCTIONS

1. Answer ALL the questions in the booklet provided.

2. Show clearly all the steps used in the calculations (SECTION B).

3. All written work must be done in blue or black ink and sketches must

be done in pencil.

ATTACHMENT: T-Table, Z-Tables, Chi-square

PERMISSIBLE MATERIALS

1. Non-programmable calculator without a cover.

THIS QUESTION PAPER CONSISTS OF 6 PAGES (Including this front page)

2 Page 2

▲back to top

SECTION A

QUESTION 1 [22 MARKS]

(Write down the question number and the letter corresponding to your best option)

1.1 A random sample of size n = 11 was selected from a population and the data are as

follows: 29,30, 45, 23, 51, 82 ,69, 12 ,71 ,65, 39. Use this dataset to answer questions

1.1.1 and 1.1.3

1.1.1 The point estimate for the mean is

[2]

50.5

46.91

45.47

47.45

1.1.2 The standard deviation of the sample mean is equal to

[2]

50.3

6.7

71.6

22.6

6.8

1.1.3. What is the range of the dataset above

[2]

1.2 Which of the following hypothesis test can be used in statistics when

n= 34ando = 29?

[2]

T-test

Z-test

one-way ANOVA

Kruskal-Wallis test

chi-square test

3 Page 3

▲back to top

1.3 A research firm conducted a survey to determine the mean amount of money steady

smokers spend on cigarettes during a week. They found the distribution of amounts

spent per week followed a normal distribution with a standard deviation of NS5. A

random sample of 49 steady smokers revealed that x = N$20 . Determine the 95%

confidence interval for pu:

[3]

(18.60; 25;40)

(19.37; 20.63)

(20; 1.40)

(19.83; 20.17)

(18.6; 21.40)

1.4 If A and B are any two arbitrary events and P(A N B) = P(A) x P(B), then the

following is true about events A and B

[2]

Event A and B are collectively exhaustive

Event A and B are mutual exclusive

Events A and B are independent

Events A and B are dependent

None

1.5

If a variable X represent the annual income per person in an organization, then X is

random variable

[2]

continuous

descriptive

discrete

normal

none

1.6

A new vaccine introduced for foot & mouth disease will either cure it or not, this is a

possible application of;

[2]

Poisson distribution

Normal distribution

Binomial distribution

Z-distribution

none

1.7 In a Poisson distribution the mean (jw) for a random variable x is the same as;

[2]

Variance (a7)

Standard deviation (c)

Number of success

Number of occurrences

4 Page 4

▲back to top

none

1.8 What is the probability of getting one success in five observations if the probability

of a success is 0.1

[3]

0.066

0.328

Cc.

0.933

0.234

none

SECTION B

(Attempt all questions and show all your working)

QUESTION 2 [46 MARKS]

2.1 The annual rainfall figures (in mm) for the past 20 years for Tsumeb are given below:

142 | 133 | 138 | 127 | 148 | 154 | 161 | 155 | 131 | 176

152 | 136 | 129 | 121 | 128 | 162 | 145 | 133 | 137 | 132

21,1

24.2

2.1.3

Determine the range for the rainfall data.

[2]

Group the data into a grouped frequency distribution with a lowest class lower limit

of 120 mm and a class width of 10 mm. (NB include class, frequency, and relative

frequency)

[7]

What percentage of the rain fall was received between 160 mm to 170 mm?

[2]

2.2

Cabbage is among the highest nitrates containing vegetarian food available in terms

of quantity. The following table present the distribution of nitrates in grams that was

measured from 29 cabbages.

Nitrates contents

(in grams)

Frequency

0-<9

9-<18

18-<27

27-<36

36-<45

2.2. Estimate the mean nitrate for the cabbages

[4]

5 Page 5

▲back to top

2.2.2 Estimate the median nitrate for the cabbages

[4]

2.2.3 Estimate the mode nitrate for the cabbages

[4]

2.2.4 Estimate the variance and the standard deviation of nitrate for the cabbages

[6]

2.3 Suppose you and a friend have contributed equally to a portfolio of $10 000 invested

in a risky venture. The income X that will be earned on this portfolio over the next

year has the following probability distribution.

$500| $100 | $2000

P(X)

0.5

0.3

0.2

2.3.1 Determine the expected value and variance of the income earned on this portfolio.

[5]

2.3.2 Determine the expected value of your share (one half) of the income.

[2]

2.4 It is known that 80% of all business startups in the IT industry report that they

generate a profit in their first year. If a sample of 10 new IT business startups is

selected, find the probability that:

2.4.1 Exactly seven will generate a profit in their first year

[2]

2.4.2 At least nine will generate a profit in their first year

2.4.3 P77 <X <8)

[4]

- [4]

Question 3 (32 marks)

3.1 You sample 34 oranges from your farm’s harvest of over 500 000 oranges. The mean

weight of the sample is 110 grams. The population standard deviation and mean are

30 grams and 115 grams respectively. What is the probability that the mean weight of

all 500 000 oranges is less than 110 grams?

[3]

3.2

During July 2018, tomatoes yield figures (in tons) were recorded over 10 farms around

Tsumeb.

Farm

B CG

Tomato yield | 35 | 21 | 33 | 24 | 30 | 36 |27 |39 | 25 | 26

(ton)

B.delis Construct a 95% confidence interval to estimate the true mean tomato yield in

6 Page 6

▲back to top

Tsumeb.

[8]

3.2.2 Is this a T-statistic or a Z statistic, and why?

[2]

3.2.3 At the 5% level of significance test the hypothesis that the mean tomato yield around

Tsumeb is below 30 ton.

[6]

3.3 The variance protein content (in mg) of a random sample of 10 bags of beans was

found to be 0.67 mg.

3.3.1 Estimate the variance for protein content of the entire population of beans with a

95% degree of confidence.

[7]

3.3.2 Can we conclude that the population protein variance for the beans is less than 1.05

mg? usea =0.05

[6]

END OF EXAMINATION QUESTION PAPER

7 Page 7

▲back to top

TABLE of CRITICAL VALUES for STUDENT'S ¢ DISTRIBUTIONS

0.25

0.765

0.741

0.711

0.706

0.700

Column headings denote probabilities (2) above tabulated values.

0.10

0.025

7.916 12:

-821 63.

0.0025 | 0.001

2.605

2.333

2.191

2.104

2.046

2.776

2.571 2.

2.447

2.365 2.5

2.306

3.747

2.998

10.214

1.948 2.228

764

718

2.1

0.0005

12)

6.869

5.959

5.041

8 Page 8

▲back to top

Cumulative probabilities for POSITIVE z-values are shown below.

.06

9983

S997

9994

9 Page 9

▲back to top

Z - Table

The table shows cumulative probabilities for the standard normal curve.

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

DOWN to the 2™ page for POSITIVE z

.03

.05

.06

.09

-3.4

0003 | .0003

4903

0003

0003 ; .0003

0003 | .0003

0003 {| .0002

-3.3

0005

.0005

0005

0004

.0004

0004

.0003

-3.2

0007

0006

0005

.0006

0008

.0005

0005 | .0005

0010

.0003

0099

0009

.0008

0008 | .0008

0007 | .0007

-3.0

0013

013

0012

0011

.0010

0010

0019 | 0018

018 | 0017 | 0016 | O016 | 0015 | 0015 | 0014 | 0014

-2.8

0026 | .0025 | 0024 | 0023 | 0023 | 0022 | 0021

0021

0020 | .0019

-2.7

0035 | .0034

0033 ; 0032 | .0031

0030 | 0029 | 0028 | 0027 | .0026

-2.6

0047

0045

0044

0043

0041

.0040

.0039

.0038

.0037

.0036

-2.5

-0062

.0060

0059

0057

0055 | 0054

.0052

0051

0049

0048

-2.4

0082 | .0080

0078 | 0075 | 0073 | .0O71

0069 | 0068 | 0066 | .0064

-2.3

0107 {| .0104

0102 |} 0099 ; .0096 | 0094 | .0091

0089 | .0087 | .0084

-2.2

0139 | 0136

0132

0129

0125}

0122

O19 | O16 | 113 | 0110

-2.1

0179 | 0174

0170 | 0166 | 0162 | 0158 | O14 | 0150 | 0146 | 0143

-2.0

0228

0222

0217 | 0212

0207

0202

0197 | .0192

0188 | 0183

193

0287

0281

274

268

0262

0256

.0250

0244

0239 | .0233

-1.8

0359 | .0351

0344

0336

0329 | .0322

0314

.0307

.0301

0254

0446

0436

0427 | 0418 | 0409 | 0401

0392 | 0384 | .0375 | .0367

-1.6

0548 | 0537 } 0526 | 0516 | .0505 | 0495 | 0485 | 0475 | 0465 | 0455

-1.5

0668 | .0665

0643 {| 0630 | 0618 | 0606 ; 0594 | .0582

0571

0559

-1.4

0808 | 0793

O778 | 0764 | 0749 | 0735 | 0721

0708 | 0694 | .0681

-1.3

0968

0951

.0934

0918

0901

0885 | .0869 | .0853

0838 | 0823

1.2

1181

134

1442

1093

1075

1056 | .1038

1020

- 1003

0985

1357

1335

A344

A292 | 1271

1251

1230 | 1210 | .1190 | .1170

-1.0

1587

1562

1639

1615

1492

1469

1446

1423

1401

1379

-0.9

1841

1814

1788

1762

1738

711

1685

. 1660

1635

1611

-0.8

2119 | 2090

2081

2933

2005 | 1977

W849 7 1922 | .1894

1867

0.7

.2420

2389 | 2358

2327 | 2296 | 2266 | 2236 | 2206 | 2177 | 2148

-0.6

2743

2709

2676

2643

2614

2578 | 2848

2614

2483

245)

-0.5

3085

3050

3015

2981

2946

2912 | 2877

.2843

2610 | 2776

0.4

3446 | 3409 | 3372 | 3336 | 3300 | 3264 | 3228 | 3192 | 3156 | 3121

-0.3

3821

3783 | 3745 | 3707

3669 | 3632 | 3694 | 3657 | 3520 | 3483

-0.2

4207 | 4168

4429

4099

4052 | 4013 | 3974 | 3936 | 3897 | 3859

-0.1

4602

A5G2

4522

4483

A443

4404

4364

4325

4286

4247

0.0

5000 | .4960

4920

4880

AB40

4801

4761

AT214

A651

4641

10 Page 10

▲back to top

APPENDIX E: The Chi-Square Distribution

,r af1p

| 995

| 0.00004

[990

| 0.00016

/i 975

:0.00098

i -950

| 0.00393

i; 900

(0.01579

| £750} 500 | «250 ' «100

050 | 025 | 010

0.10153 (0.45494 |1.32330 |2.70554 [3.84146 |5.02389 |6.63490

605

7.87944

r"2. af [0.01003 [o.oz010 0.05064 0.10259 0.21072 0.57536 {1.38629 j 2.77259 14.60517 :5.99146 [7.37776 (9.21034 |10.59663 |:

3 [oon [0.11483

|0.20699 fo29711

| 0.41174 | 0.55430

0.67573 {0.87209

“0. 9926 s 1.23904

\\(1.3444) ‘}1.64650

(0.21580

‘0.48442

(0.83121

| 1.23734

“1.68987

2.17973

0.35185

0.71072

‘114sag

| 1.63538

2.16735

[2.73264

[0.58437

(1.06362

1.61031

[1.21253 |2.365

[1.92256 [3.35669

| 2.67460 [4.35146

‘4.10834 6.25139

| 5.38527 |7.77944

| 6.62568 | 9,23636

‘7.81473 (9.34840 | 11.34487 | 12.83816 {{{

9.48773

*11.07050

{1.14329

| 12.83250

| 13.27670

} 15.08627

| 14.86026

16.74960

|{i:

+ 10.64464 (2.2a 0413 |3.45460nnn p5.a34c81e2s + 7.t 840n 80 eo

li p1e2n.n59an1ne59 |Ro1s4e.ni4e4r9o3a8te | 1f6.a8t11a89 |pet1e8.54S7E58

2.83311 [4.25485 } 6.34581 {9.03715 $12.01704 | 14.06714 | 16.01276 | 18.47531 | 20.27774

1 3.48954 [5.07064 {7.34412 :10.21885 | 1i 13.36157 | 1 30731 1 17.53455 | 20.09024 [21.9549

{2.08790 123 70039

(2.15586 [2.55821

{2.60322 |3.05348

{3.57087 4 40379

3.32511 i 16816 iS: 89883 8.34283 |_ 11,38875 | 14.68366| ; 16.91898 119. 02277 j2 66599 |23.58935 |

(3.94030, |4.86518 |6.73720 _[psaa [iaseeds | 1s98718 | 181:8.30704 |

4.57481 | 5.57778 i7seaa 1 10.34100 |' 13.70069 | {7.27501 | |19.67514 | 21.92005 24.72497 Eosal |

|5.22603| 2829952 | le5..30380 “fs 43842 i 11.34032: (14.8844540 1i| 8. 15493: 1. 02607 123. 33666 | 26.21697

1433 a 56503 + 10692 |5.00875 | 5.89186 ' 7.04150 !9.29907 | 12.33976 !15.98391 /19.81193 “| 2236203 | 24.73560 127.6825 29.81947

i 14 «(40707467

“5.62873 | 6.57063 | 7.78953 {0.16531 {13.33927 1711693 |21.006644114 | 23.68479 |26.11895 [29. 14124 [31.31935

| 4.60092

| 6.26214 i 7.26094 18. 54676 f 11.03654 i 14.33886| 18.24509 (22. 30713 |24.99579 (27, AB839 |'30. S7791 j32. 80132,

1514221 Ciel "6.90766 i7.96165 “931224 11,91222|j 1s. 33850| 19.36886; | 23.54183| | 26.29623 128. 84535 3| 99993 [3426719 |

| 5.69722 6.40776 )7.S6419 8.67176 ,10.08519 | | 12.79193 "1633818 | 20.48868 | 24.76904 }27.58711 £30.19101 (35.4086 [35.71847

| (2200

{6.26480

{6.84397

| 7.43384

sapo7ns.n6e0e31a24l79313

8.23075: 9.39046 "10.86494 | 13.67529 | 17.3790 | 21.60489| 25.98942 | 28.86930 | 31.52638 [34 80531 |37.15645 i

[anes |“/10.11701 /11.65091 [14scan0 vassies | 2.1781 |"7.20357| 0.14353 |32.85233| 36.19087 (38. 58226 |

9 28. 41198 a 41043 /34, 1696 7.56666223 [399.96585 |

Pa21 8.03365 ha 1| 10.28290| ‘it -59131 | 13.23960 fie 34438 20.33723 |124, 93478 29.61509 |}32, 67057 |135. 47888 (3a 93217 }41.400110066 |

8.64272 [osazas (To.98232 | 1 12,3380! | 14,04149 {17.23962 | 21.33704 (3603027 - 30.81328 /33.92444 (36.78071 /40.28936 142.79565

| 23 |9.26042 } 10.19572 | 1.68855 | 13.09051 | 14.84796 | 18.13730 | 22.3688 27.14134 |32,00690 | 35.17246' 38.07563 |41.63840 [44.18128

| 24 {9.88623 fio 85636 4; 12. 401 5; | 13. 84843| | 15.65868 H19.03725 |123. 33673; 28.24115 : : 33.19624| 136. 41503 139. 36408 [4297987982. |45. 55851

|| 2255 | 10.51965 | 11.5298 | | 13.1197 14.61 141 \\ 16.47341 1i9. 93934 (24, 33659 9. 33885 | 4.38159. {31 65248| 40.64647 |44.31410 [46.92789.

26 j1l..1610602244 [12.1 1981| 5 13,8439 }¥55..37916 || 7. 29188 [ao8e4343 | (25. 133646 | 30. 43457 | 135, 56317, 138.88514 |(41.92317 [14455,64168g | 48. 28988

127 111.8079 fraa7es0_ , 14.57338 +16.15140 18.1390 |21.74940 } 26.33634 ,31.52841 | 36.74122 F40.11327 1| 43.19451 } 46.96294 |49.64492

28 {12.46134 | 13.56471 | 15.30786 | 16.92788 | 18.93924 | 22.65716 |27.3623 |32.62049 |37.91592 |41.33|447.4160479 | 48.27824 |50.99338

——

£29 113.12115

14.25645 | 166.04707

|"17.70837 | 19.1674 |23,56659| 28.33613{33.71091 |39.08747 {42.55697 |45.72229 | 49.58788 [52.33562

130 |13.78672' [ra9s34 | (16.7907| | 18.49266;20. 59923 (24, 47761 [299.33603 . 34, 194 140. 25602 (4(43.77297 |146. 97924 |}50.89218 [53. 67196 ,

Page 7 of7