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BBS112S - BASIC BUSINESS STATISTICS 1B - 2ND OPP - JAN 2023 |
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nAmlBIA
un1VERSITY
OF SCI En CE Ano TECH n OLOGY
Faculty of Health, Natural Resources and Applied Sciences
Department of Mathematics and Statistics
QUALIFICATIONS:B. Business Admin, B. Marketing, B. Human Resource Management, B. Public
Management and B. Logistics and Supply Chain Management
QUALIFICATIONCODES:21BBAD / 07BMAR /
07BHR / 24BPN / 07BLSM
LEVEL: 6
COURSE: BASICBUSINESSSTATISTICS1B
COURSECODE: BBS112S
DATE:JANUARY2023
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
SUPPLEMENTARY/SECONDOPPORTUNITYEXAMINATION QUESTION PAPER
EXAMINER(S)
MR E. MWAHI, MRS. KASHIHALWA, MR I. NDADI MS. Y NKALLE, MR A. ROUX,
MS L. KHOA, MS A. SAKARIA
MODERATOR:
MRJ. SWARTZ
THIS QUESTIONPAPERCONSISTSOF 5 PAGES
(Including this front page)
INSTRUCTIONS
1. Answer all the questions and number your solutions correctly.
2. Question 1 of this question paper entails multiple choice questions with options A to
D. Write down the letter corresponding to the best option for each question.
3. For Question 2, 3 & 4 you are required to show clearly all the steps used in the
calculations.
4. All written work MUST be done in blue or black ink.
5. Untidy/ illegible work will attract no marks.
PERMISSIBLEMATERIALS
1. Non-Programmable Calculator without the cover
ATTACHMENTS
1. Standard normal Z-table and the Chi-square table.
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QUESTION 1 [20 MARKS]
Write down the letter corresponding to the best answer for each question.
1.1 When the population is divided into mutually exclusive sets, and then a simple random
sample is drawn from each set, this is called:
[2]
A. Simple random sampling.
B. Stratified random sampling.
C. Cluster random sampling.
D. Systematic random sampling.
1.2 A marketing research firm divides the population of a state into geographic areas, and
randomly selects some of the areas and takes a simple random sample of each
selected area. This is an example of a
[2]
A. Cluster random sample
B. Systematic random sample
C. Simple random sample
D. Stratified random sample.
1.3 Laspeyres index formula uses the weights of the ................... ..
[2]
A. Base period.
B. Current year.
C. Average of the weights of a number of years.
D. None of the above.
1.4 A manufacturer of contact lenses is studying the curvature of the lenses it sells. In
particular, the last 500 lenses sold had an average curvature of 0.5.
The population is
[2]
A. The 500 lenses.
B. 0.5.
C. The lenses sold today.
D. All the lenses sold by the manufacturer.
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1.5 A political scientist is studying voters in California. It is appropriate for him to use a
mean to describe:
[2]
A. The age of a typical voter.
B. The party affiliation of a typical voter.
C. The sex of a typical voter.
D. The county of residence of a typical voter.
1.6 A researcher is studying students in college in California. She takes a sample of 400
students from 10 colleges. The average age of all college students in California is? [2]
A. A statistic.
B. A parameter.
C. The median.
D. A population.
1.7 The standard deviation of a normal population is 10. You take a sample of 25 items
from this population and compute a 95% confidence interval. In order to compute the
confidence interval, you will use
[2]
A. The t table because the degrees of freedom will be 24.
B. The t table because the sample standard deviation is known.
C. The z table because the population standard deviation is known.
D. The z table because the sample size is small.
1.8 If in a random sample of 400 items, 88 are found to be defective. If the null hypothesis
is that 20% of the items in the population are defective, what is the value of the test
statistic?
[2]
A. 0.02
B. 1
C. 0.9656
D.1.03
1.9 A 92% confidence interval for population proportion is 32.4% to 47.6%, the value of
sample proportion is:
[2]
A.40%
B. 32.4%
C. 47.6%
D. 80%
1.10 In a simple random survey of 89 teachers of high school AP Statistics, 73 said that it
was the most satisfying, most enjoyable course they had ever taught. Establish a 98%
confidence interval estimate of the proportion of all high school AP Statistics
teachers who feel this way.
[2]
A. 0.820 ± 0.004
B. 0.820 ± 0.041
C. 0.820 ± 0.084
D. 0.820 ± 0.095
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QUESTION 2 [29 MARKS]
2.1 Suppose you would like to estimate the mean teacher's salary in Khomas region
, with 99% confidence, to an accuracy within N$2000. You are told that the
population standard deviation of teachers' salaries in Khomas is known to be N$6000.
Find the necessary sample size you will need for this study.
[3]
2.2 Suppose scores on exams in statistics are normally distributed with an unknown
population mean and a population standard deviation of 3 points. A random sample
of 36 scores is taken and gives a sample mean score of 68 points. Find a 90%
confidence interval estimate for the population mean exam score.
[5]
2.3 Suppose a baker claims that his bread height is more than 15 cm, on the average.
Several of his customers do not believe him. To persuade his customers that he is right,
the baker decides to do a hypothesis test. He baked 10 loaves of bread. The mean
height of the sample loaves is 17 cm. The baker knows from baking hundreds of loaves
of bread that the standard deviation for the height is 0.5 cm and the distribution of
heights is normal. Help the baker do his hypothesis at 1% level of significance. [8]
2.4 With individual lines at its various windows, a post-office is interested in the standard
deviation for normally distributed waiting times for customers on Friday. The post-
office experiments with a single main waiting line and find that for a random sample
of 25 customers, the waiting times for customers have a variance of 12.25 minutes.
2.4.1 With a significance level of 5%, construct a confidence interval estimate for the
variance waiting times of all customers at this post-office on a Friday.
[6]
2.4.2 Assuming that the estimated population variance at this post-office is 51.84 minutes,
is there evidence at 1% level of significance to conclude that a single main waiting
line causes lower variation among waiting times for customers?
[7]
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QUESTION 3 [32 MARKS]
3.1 A sample of 870 NUSTstudents was asked for their preferences of one of the three
ice-cream flavours (chocolate, vanilla and strawberry). The results are summarised in
the contingency table below:
Gender
Flavour
Chocolate
Vanilla
Strawberry
Men
100
120
60
Women
300
200
90
At 5% level of significance, is there evidence to conclude that gender influences ice-
cream flavour preference?
[12]
3.2 The data on the table below shows the yield of maize per hectare in 100kg bags at
Etunda irrigation project in Omusati region over the period 2003-2013.
Year
Yield
(100 kg)
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
24 19 36 32 26 34 26 26 29 38
2013
30
3.2.1 Compute a 4-period centred moving average trend for the time series.
[7]
3.2.2 Compute the straight line trend equation (Y = a + bX) by the method of least squares
using the sequential coding method, start the coding from 1 (x=l for 2003).
[10]
3.2.3 Estimate the yield of maize per hector in 100kg bags for the year 2017.
[3]
QUESTIONSTION 4 [19 MARKS]
In Oshakati town the monthly food expenses of a typical family between the year 2000 and
the year 2004 were as following:
Product
Measurement
2000
2004
Quantity
Price (N$)
Quantity
Price (N$)
Bread
kg
18
94
25
110
Milk
litre
32
86
44
130
Salami
dkg
300
74
380
81
Using the year 2000 as the base period, answer the following questions:
(a) Find the simple aggregate quantity index and interpret your results.
[5]
(b) Calculate the Laspeyres price index and interpret your results.
[7]
(c) Calculate the Paasche quantity index and interpret your results.
[7]
=============END OF EXAMINATION===========
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0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
-2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
u
0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
u
0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
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0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
u
0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
u
0 6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
-2.4 0 0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
u
0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
u
0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
u
0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
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-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
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1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
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-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 00314 0.0307 0.0301 0.0294
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
-1.6 0.0548 0.0537 0.0526 0.0516 0 0505 0.0495 0.0485 0.0475 0.0465 0.0455
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
-1.5 0.0668 0 0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
-1.3 0.0968 0 0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
u
0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0 9803 0.9808 0.9812 0.9817
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
LI 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
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0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0 4404 0.4364 0.4325 0.4286 0.4247
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
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APPENDIX E: The Chi-Square Distribution
df\\p •: .995
.990
.975
ii .950 . .900
.75o ; .5oo
.250
.100
...............,. .............-..·.-.·····
.................-...,........-... ----·············•··••········"·
·········••··."."." .........
1 0.00004 '1?·°..°.0°..0100.9~8. :0.00393 ilo.01579 :0.10153 ;10.45494 ,_1.32~3°..i 2.70554
i 2 ·0.01003·: :o:02·010··.o.o5o64 •lo.10259 io.21072 :jo.57536 ,ii3ai29··12:7i2i· ir:;~iiiis:1S:799·1·416..
.025
5.02389
.010
.005
6.63490 i:7.87944
9.21034 1[10.59663
3 . l0.07172 ·jo.11483 :?-~1.5.80 'lo.35185 l!?-~.8437 111.21253 [2.36597 l:4.10834 ·1!6.25139 ::7.81473 i9:34840 i 11.34487 ![i2:83816 ·•·
4 0.20599 ilo.29711 o.48442 :lo.71072 h.06362 11.9225·6··,!3·.·35·6·6·9.·.·.:''·.5·..3·.8.·5.•2.7·..··.·b.·..·.7.'.7·..9·..4.·.4..·..·...·J..·.·9.....4..8..7..7.3..I•.·1.=1...1.=4.3.~2.9.-:.-.1.-3..~2.7.-6..7-.0~.':.1.4...8.6026
5 0.41174 :i?:~.5~~?. :a.:8.?.~~1-.)u4548.J!1.61031 [2:6?.~~?-~}.35146 6:~~.5.~~.'.9~~.~.36 . 11.07050 1_1-~.:.8?.~5.?J15.:°.~?.?7.::~~-74960
,,
,·
6 o.67573 :o.87209 ,1.23734 ).63538 li2.20413 !3.45460 15.34812 :7,84080 ::10.64464 I 12.59159 I 14.44938 ; 16.81189 :\\18.54758 ;
.o.98926· l[1..~}.~~~i 7
11.23904- ·;68987 l2:1.~?.3}J2.83311 i4.25485 J6.34581 !9.03715
I.i4.O6?14l1G:0.iiiGli'a.4753.~J~o.27774
•·•·•·••···········.·.•.·....................
8 1.34441 '1.64650 2.17973 .:2.73264 ;13.48954 '5.07064J7.34412
!Jo.21885 !i13.35157 h5.50731 l 17.53455 I 20.09024 i:21.95495
9 ,1.73493 :2.08790 i2.70039 13.32511 tl4.16816 15.89883 18.34283 1:11.38875 1114.68366 1!16.91898! 19.02277 I 21.66599 1:23.58935
!i
.-1-~-.2~.155~~·i:-2.5582~... '3.246~~:~940~0_
--
----
•-·,:···
11 2.60322 13.05348 :3.81575
:/4.86518 ._ !~:~~~.?
h~.548~~. !!1~~~~~_! !1.~~?7-?~.~1o~~~318_!_2~~2.02_!:2~55...1~~~..
.
,. ··-
'
12 3.07382 •3.57057 4.40379 :5.22603 il6.30380 :8.43842 ill.34032 <14.84540 i:18.54935 1'21.02607 23.33666 I 26.21697 i 28.29952
. ···-··
i I ! 13 3.56503 !4.10692 5.00875 15.89186 117.04150 19.29907 li2.33976i.15.9B391 ['19.81193 22.36203 24.73560 27.68825 ,;29.81947
- - - -
- .- - . ---- .- -- ---
- ·--. ---·- --·- ·- -·-
··- -· --- ·------·· -------•-- .. --- ---------- --- - -
14 4.07467 4.66043 '5.62873 :6.57063 l\\7.78953 10.16531 ,[13.33927117.11693 [21.06414 / 23.68479 26.11895 j 29.14124: 31.31935
i i 15 4.60092 !5.22935 6.26214 :7_26094 8.54676 111.03654·114.33886: 18.24509 ,!22.30713 24.99579
······--·······················
··························''·························-··········-·
==-c:--:-~
16 5.14221 •!5.81221 '5_9·07,:·76.966165 119.31224 '!11.91222 J1s.33aso L19.36886 !/23.s41a3 !:26.29623
17 '5.69722 i6.40776 7.56419 ,!8.67176 !i10.08519 !i12.79193 !16.33818 ;·20.48868 i:24.76904 ;!27.58711 j 30.19101
i 18 '6.26480 l7.01491 18.23075 i19.39046 l!io.864941 I13.67s29 1!i7:3i7iio Ibi:6o4a9 :25.98942 i'28.86930 1·31.52638
i 19 6:84397-::7.63273 !-8.-90-6-521- 0.11701 !!11.65091:114.56200:118.33765l-:22-.7-1-78-1~!'27:2oli[5io7.14353 32.85233
.............................!.l. ...........,............... ,i .....•............. ,........ \\ .........................
;: ............................. •\\ ................................ :· ............... , ............ ,, .... ·••··
! ! 20 7.43384 •!8.26040 9.59078 ..:!!0·8.5.°.~1]l~:~~2~1 !!15..4sxf;;·:!i?.)37,~3. ?3.:8!?~?1 :?8.:~l~?~ j:3.1.41?~3/ 34.16961
..2..i._.:_·_a.-O:i3fB65~-B--:97t1-0:.i2O82-90 i r1i.s9131 !I13.23960 ;!16.3M3a !20.33723 I:24:93..4.7..8... ;.
. i ! .. --·····-···
22 8.64272 .:9.54249 10.98232 :112.33801 ![14.04149 :117.23962
23·9:26042 · '10.19572 11.68ass.Jiio9051 !ii4.84796 '118.13730 fiiiiG.ss"12;,:14134 h2.00690 135.17246
41.63840 i:44.18128
i 24 9.88623 :,10.85636 12.40115 ,j13.84843 jj15.65868 :119.03725 i23.33673l28.241151·33.19624 J;35.41503 39.36408 42.97982 ;'45.55851
25 '10.51965 :111.52398 n11972 14.61141 i!16.47341 19.93934. 24.33659 ,29.33885 34.38159 .37.65248 40.64647 44.31410 · 46.92789
,.:!
:.
26
'11.16024 ;!12.19815
13.84390
;!15.37916 i)
7.29188
:i-20-.-84-3-i4235~.3,3646 i
30.43457
iii5:56317
0
i 38.88514
i 41.92317.i
45.64168
; ;48.28988
;
27 :11.80759 112.87850':14.57338,[16.151401118.11390 '[21.74940 '126.33634if31.52841l°36.741221'40.11327: 43.19451 i 46.96294] 49.64492 ·:
..-. ·=:::..-·:::.:-.:.::::__. ,- ·---· ·--- ··---···•-·---
.---·····.;·,::::.:.::;..:.:-.._··-;·.-:-.·_·-·-:-<-···:·::··-·. ....... ··.. ;._.:..-............-..-.·..,... --·•-··-:··..:.·:.~_-.=:_:._·.:__..·:.:._·.-,-.··:----· ........".'..,. ............·.-.•..-.-.-.·••--.·.--
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