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BBS112S - BASIC BUSINESS STATISTICS 1B - 1ST OPP - NOVEMBER 2023 |
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. nAmlBIA UnlVERSITY
OF SCIEnCEAnDTECHnDLOGY
FacultyofHealth,Natural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: +26461207291~
E: msas@nust.na
W: www.nust.na
QUALIFICATION: B. Business Ad min, B. Marketing, B. Human Resource Management, B.
Public Management and B. Logistics and Supply Chain Management
QUALIFICATION CODE: 21BBAD / 07BMAR / 07BHR /
24BPN / 07BLSM
LEVEL: 6
COURSE:BASIC BUSINESS STATISTICS lB
COURSECODE: BBS112S
DATE: NOVEMBER 2023
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
FIRST OPPORTUNITY: EXAMINATION QUESTION PAPER
EXAMINERS: MR E. MWAHI, MRS. KASHIHALWA, MR J.AMUNYELA, DR.J. MWANYEKANGE,
MRS A. SAKARIA,MS. N. PONHOYOMWENE,MRS L. KHOA
MODERATOR: MR J. SWARTZ
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.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator
ATTACHEMENTS:
1. T-Table
2. Normal distribution table
3. Chi-square table
This paper consists of 5 pages including this front page.
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QUESTION 1
[10 MARKS]
1.1 The mean is:
[2]
A. a summary of some data estimated by adding all the numbers and dividing by the
number of observations minus one.
8. a summary of the data that is a measure of the population rather than a sample.
C. a summary of some data that is always halfway between the maximum and
minimum value of the data.
D. none of the above
1.2 If data show "homogeneity of variance", it means that:
[2]
A. They must be analysed with a chi-square test.
8. Scores in each group or condition show comparable amounts of variance.
C. The data are normally distributed.
D. They have been measured on an interval or ratio scale.
E. None of the above.
1.3 If you perform a one-tailed statistical test, your hypothesis is:
[2]
A. That the experiment was conducted double blind.
8. That the difference between your groups will be in a specific direction.
C. That the two different measurements are unpredictable from each other.
D. That the variance of two measurements does not differ significantly.
E. That the mean of two measurements does not differ significantly.
1.4 A type II error:
[2]
A. Is when one rejects the null hypothesis when in fact is true.
8. Is when one accepts the null hypothesis when it is false.
C. Is always the result of bias in the sample.
D. Is the error of using the wrong test.
E. ISthe error of using the same data twice.
1.5 If a sample is unrepresentative, this implies:
[2]
A. That not enough data were collected.
8. The data are not normally distributed.
C. That one single measurement was not typical and therefore not useful.
D. That the sample should not be used to make inferences about the population.
BASIC BUSINESS STATISTICS lB
pt opportunity November2023
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QUESTION 2
[36 MARKS]
2.1 New Edge Investment Trust gives each of its employees an aptitude test. The scores
on the test are normally distributed with a mean of 75 and a standard deviation of 15.
A simple random sample of 25 employees is taken from this population.
2.1.1 What is the probability that the average aptitude test score in the sample will
be between 72.13 and 80.13?
[6]
P(~ c) 2.1.2 Find a value C, such that
= 0.0571
[4]
2.2 The operation manager wants to have 90% confidence of estimating the proportion
of nonconforming newspapers to within ±0.05 of its true value. In addition, because
the publisher of the newspaper has not previously undertaken such a study, no
information is available from past data. Determine the sample size.
[5]
2.3 The personnel department of a large corporation wants to estimate the family dental
expenses of its employees to determine the feasibility of providing a dental insurance.
A random sample of 10 employees reveals the following family dental expenses for
the year 2020.
110 362 246 85 510 208 173 425 316 179
2.3.1 Find the sample mean of these family dental expenses.
[2]
2.3.2 Find the sample variance of these family dental expenses.
[3]
2.3.3 Construct a 95% confidence interval estimate of the true population variance
of family dental expenses.
[6]
2.4 The table below shows data on type of school area and the student's choice of good
grades, athletic ability, or popularity as most important.
Goals
Good grades
Athletic ability
Popularity
Urban
24
6
5
Type of School Area
Suburban
87
42
22
Rural
57
50
42
At the 5% level of significance, is there a relationship between the type of school area
and the student's choice of good grades, athletic ability, or popularity as most
important?
[10]
BASICBUSINESSSTATISTICSlB
1st Opportunity November 2023
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QUESTION 3
[ 26 MARKS]
3.1 When constructing the confidence interval limits for the population mean, the width
of the interval is influenced by three factors. List down these three factors.
[6]
3.2 A survey of a random sample of 300 grocery shoppers in Otavi found that the mean
value of their grocery purchases was N$78.00. Assume that the population standard
deviation of grocery purchase values is N$21.00. Find the 95% confidence limits for
the average value of a grocery purchase by all grocery shoppers in Otavi.
[6]
3.3 A Spar retailer observed a random sample of 160 customers and found that 68
customers paid for their grocery purchases by cash and the remainder by credit
card. Construct a 95% confidence interval for the actual percentage of customers who
pay by credit cards for their grocery purchases.
[6)
3.4 The manager of a large shopping mall in Mariental believes that visitors to the mall
spend, on average, 85 minutes in the mall on any one occasion. To test this belief,
the manager commissioned a study, which found that, from a random sample of
132 visitors to the mall, the average visiting time was 80.5 minutes. Assume a
population standard deviation of 25 minutes and that visiting time is approximately
normally distributed. Conduct a hypothesis test for a single mean at the 5%
significance level to support or refute the manager's belief.
[8]
BASICBUSINESSSTATISTICS1B
l51 0pportunity November 2023
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QUESTION4
[ 28 MARKS]
4.1 A hotel's monthly occupancy rate (measured as a percentage of rooms available) is
reported as follows for a 10-month period:
Months
Jan Feb Mar Apr May Jun July Aug Sep Oct
Occupancy 74
82
70
90
88
74
64
69
58
65
4.1.1 Construct a 2-period centred moving average for the occupancy rate. [7]
4.1.2 Fit a least squares trend line to the hotel occupancy rate data using the
sequential numbering method, start coding with 0.
[8]
4.1.3 What is the trend estimate of the hotel's occupancy rate for December? [3]
4.2 The data in Table 13.8 refers to a basket of three carpentry items (cold glue, wooden
boards and paint) used by a joinery company in the manufacture of cupboards for
2010 and 2011 respectively. The data was collected from the company's financial
records.
Carpentry
Cold glue
Boards
Paint
Year 2010
Price
Quantity
N$13
45
N$63
122
N$122
16
Year 2011
Price
Quantity
N$15
52
N$77
110
N$125
20
4.2.1
Using the Laspeyres weighted aggregates method, construct a composite
quantity index for the average change in the quantity of carpentry materials
used between 2010 (as base period) and 2011.
[S]
4.2.2
Using the Paasche weighted aggregates method, construct a composite
quantity index for the average change in the quantity of carpentry materials
used between 2010 (as base period) and 2011.
[S]
=============END OF EXAMINATION===========
BASIC BUSINESS STATISTICS lB
l51 0pportunity November 2023
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• •p
.....
-
-,
.......
,.
Ie.g.. for z" - 1}4, refer t? the - ·1.3
row and the0.04 column to
r~-· find thecun1uiaavco.reu0::0901.
The Standard Normal Distribution
0
z
0.00
0.0,
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
-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
-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
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
©.
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
-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
-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
-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
Source:Cumulativestandardnormalprobabilitiesgeneratedby Minitab,then roundedto four decimalplaces.
I 5217X_IBC.lndd 1
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-· ... -- .,
e.g .• for z = 1.34. refer to the,
1.3 row and the ·o.04columnto
find the cumulativenre110..9099.
The StandardNormal Distribution
0
z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
§)
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
®.
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
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
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0
0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
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APPENDIX D: The t-distribution
df\\p
0.40 1· 0.25 II 0.10
.:I 0.05 I[_ 0.025·--·-c~~-:~-~- _..11 0.005
0.0005 ·:
1 '10,324920 1:"i.000000 :13.077684 1:6.313752 1112.70620 'j31.82052 . ·1:63.65674 636.6192
··7 2 _:[o.288675 Jo.816497 ___jJ1.88S618_ ·1:~.:~-~~-~_~?j4.30265- __j_6_._96456
9.92484 · ___;31.5991.. ···.·-.··
1
3
Jii.-924-0-·-·-- [o.276671 J.o.764892 ___1[1.637744 -; 2.353363 :13.18245 1[4.5407o 115.84091
·,0270722 4
]:o.740697 - ·111·.s33206 [.2.131347 [!2.77645 ',3_74595 114.60409- [8.6103
5 :lo.267181
6
1, 0:264835
[---···7 --[o.263167
1:o.726687 :11.475884 1•2.015043 l\\2.57058
3.36493
l!o.717558 ·11.439756 1.1.943180 ___12.44691 ·13.14267
1
[2::i6462 110.711142 lilA149-24·---h894579 .......
12.99795
114.03214
113.70743
jt3.49948
===== 16.8688
5.9588
15.4079
L.....~-----:lo.261921
1
I 0.706387 J[l.396815 :1.859548 ,12.30600
12.89646 ir~:.~5539 tl5.0413
,--- 9·---- ..:0.260955 ]:0.702722
1[1.383029 1-1~a33"J:13-·112.26216 2.82144 ... 1~24984 ..........[.4.7809
, 10 Jo.260185
l:o.699812 ·11.372184 I 1.812461 1[2.22814
,2.76377
113.16927
14.5869
1
1
11
·-·110·?-59556·-··1,o 697445
11363430
"
Ji1 795885
!I-?·?-0099
1271808
1i,3•10581 · 4.4370
I 12 .10,259033 110.695483 111.356217 ![1.782288 ,J2.17881 .12.68100 1[3.05454··-----'14,3178
I
13
If 10,258591 1·0.693829
"1
1.3?_°._1!._]~ !_:_770933 ![2.16037 ____,2.65031
1~.01228 .. __ 14.2208
·I
I
I 14
lo:258213 1o.692417 111.345030 11.761310 ·112.14479
'*•- ..----·-··· ....-,,-- ..·-----·····, _ ........._.,
I 15
,0.257885
I
1:0.691197 i/1:340606
i2.62449
..._.._
1'2.97684
112.94671 ---
-1,44.14~05072-.·8..I·.·,·~~--
I 16 10.257599
..
l'o.69-0132
!11.336757
!'1.745884
I 17 i!o.257347 J.0.689195 11.333379 . -·1i1.739607
I 18
I
I 19
·110.257123
:10.256923
jio.688364
1o.687621
!11.330391
IJ1.32n28
I 1.734064
; 11.729133
:b.11991 '12.58349
....·1....
1[2.10982 1[2.56693
112.92078
112:89823
IJ2.10092 112.55238 ![:i:-87844
112.09302 !2.53948 ··-] [2.86093
14.0150
...
,3.9651
......,... ..I.
i3.9216
,!3.8834 - --1
I 20
I 21
·10.256743 1o.686954
0.256580 i'o.686352
111.325341 I 1.724718 1:2.08596
111.323188_______1!1.720743 12.07961
: 2.52798
:12.s1765
1
1~84534 . ' 3.8495
···1 112.83136 '@,8193...
22 :10.255432 l·o.6858os_J[1.321237
11.717144 !12.07387 :2.so332 [12.81876 :13_7921
l....... 23
I
I
24
lo.256297
..,
I 0.256173
.,.._,
j:o.685306
l:o.684850
![1:319460
'11.317836
I 1.713872 "'112,06866
1:1.710882 1!2.06390
,12.49987 lb.80734
!12.49216 112.79694
13.7676
·J3.7454
.t
I 25
,0.256060 110.684430 111.316345 111.708141 [2.05954
112.48511
il2.78744
1· •
;13.7251
I
I 26
I 27
I 28
llo.255955 ... ];o.684043
:10.255858 1:0.683685
:
0.255768 1:0.683353
111.314972 1,1.705618
111.313703 1,1.703288
111.312527 1·1.701131
1[2.05553
1[2.05183
112.04841
I
,2.47863
:12.47266
1[2.46714
lb.77871
112.77068
112.76326
).7066
I 13.6896___ ·-· I
13.6739
! 29
110.255684 1o.683044 111.311434 : 1.699127 1!~:04523
[2.46202
1:2.75639
[3.6594
I
I 30
10.255605 II o.682756 1/u10415
1:1.697261 ;12.04227 112.45726 l12.75000 !r3:.-6-4-6-0·
'
I
I inf io.253347 [·o.674490 111.281552 111.644854 ;[1.95996 '12.32635 112.57583 ,13.2905
'
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..'.'
APPENDIX E: The Chi-Square Distribution
'.~...1-·.995·-.1:;1;;;···--·;-]·:I;;.9755011-·:900-r·:1-7so[·sool-l··.2501-1""":l·o1"1.o050i,-·:·o··i1s· :oio1'"1····.·o·o·1s
,1 _,_:0.000l0lo4.000i106.000J9l8o.00319130.01151709.10!1lo5.3454J9!u4233l0p.705]5143.8411456.o2319:96.634[j970.879l44
2 1'0:0~01~;39.9_2to~.10050l~[o_._1[l0o2.2~10l7fo2:_~2.~.1.~.61:3_.181~2.97-7l2l~5-960511175.99l1,74.6377]796.2_1._1.:0.913·4_5_9.~~3]
,:3...;o.07172~]10T.1o1.42813l?_~s:_~s-_1ia~o~~]_~]31!]1.212I[523.'.~~Jl~~?:._.71-o[_~~~1~-_~lJ7_-i-]~.1~-~...1-_~:3.~11~2~.°8-3]:8_116_.1:_3
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