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BBS112S - BASIC BUSINESS STATISTICS 1B - 1ST OPP - NOV 2022 |
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nAmlBIA
OF SCIEnCE
unlVERSITY
TECHnOLOGY
Faculty of Health, Natural Resources and Applied Sciences
Department of Mathematics and Statistics
QUALIFICATIONS:B. Business Ad min, B. Marketing, B. Human Resource Management, B. Public
Management, B. Logistics and Supply Chain Management
QUALIFICATIONCODES:21BBAD / 07BMAR /
07BHR / 24BPN / 07BLSM
LEVEL: 6
COURSE: BASICBUSINESSSTATISTICS1B
COURSECODE: BBS112S
DATE: NOVEMBER2022
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
EXAMINER(S)
MODERATOR:
FIRSTOPPORTUNITYEXAMINATION QUESTION PAPER
MR. E. MWAHI, MR. I. NDADI, MR. S KASHIHALWA, MS. L. KHOA, MS. Y. NKALLE,
MS. A. SAKARIA
MR.J. SWARTZ
THIS QUESTION PAPER CONSISTS OF 7 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.
PERMISSIBLE MATERIALS
1. Non-Programmable Calculator without the cover
ATTACHMENTS
1. Standard normal Z-table, t-table and the Chi-square table
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QUESTION 1 [30 MARKS]
Write down the letter corresponding to the best answer for each question.
1.1 You take a random sample from some population and form a 96% confidence
interval for the population mean, which quantity is guaranteed to be in the interval
you formed?
[2]
A.O
B. µ
C. x
D. 0.96
1.2 What should be the value of z used in a 92% confidence interval?
[2]
A. 2.70
B. 1.75
C. 1.81
D. 1.89
1.3 Why do we use inferential statistics?
A. To help explain the outcomes of random phenomena
B. To make informed predictions about parameters we don't know
C. To describe samples that are normal and large enough (n>30)
D. To generate samples of random data for a more reliable analysis
1.4 Statistics and parameters ....
A. Are both used to make inferences about x
B. . Describe the population and the sample, respectively.
C. Describe the sample and the population, respectively.
D. Describe the same group of individuals.
1.5 To test for equality of two population variances, one would use the ___
[2]
[2]
test. [2]
A. z
B. t
C. Chi-square
D. F
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1.6 A null hypothesis was rejected at level alpha=0.10.What will be the result of the test
at level alpha=0.05?
[2]
A. Reject Ho
B. Fail to Reject Ho
C. No conclusion can be made
D. Reject Ha
1.7 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. 0.22
1.8 A ____
is a range of numbers inferred from the sample that has a certain
probability of including the population parameter over the long run.
[2]
A. Hypothesis
B. Lower limit
C. Confidence interval
D. Probability limit
1.9 The null and alternative hypotheses divide all possibilities into:
[2]
A. Two sets that overlap
B. Two non-overlapping sets
C. Two sets that may or may not overlap
D. As many sets as necessary to cover all possibilities
1.10 What is the standard deviation of a sampling distribution called?
[2]
A. Sampling error
B. Sample error
C. Standard error
D. Simple error
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1.11 What does it mean when you calculate a 95% confidence interval?
[2]
A. The process you used will capture the true statistic 95% of the time in the long run
B. You can be "95% confident" that your interval will include the population parameter
C. You can be "5% confident" that your interval will not include the population
parameter
D. All of the above statements are true
1.12 What is the key question in the field of statistical estimation?
[2]
A. Based on my random sample, what is my estimate of the population parameter?
B. Based on my random sample, what is my estimate of normal distribution?
C. Is the value of my sample statistic unlikely enough for me to reject the null
hypothesis?
D. There is no key question in statistical estimation
1.13 When the researcher fails to rejects a false null hypothesis, a __ error occurs. [2]
A. Type I
B. Non-sampling
C. Type II
D. Sampling
1.14 __ is the difference between a sample statistic and the corresponding population
parameter.
[2]
A. Standard error
B. Sampling error
C. Difference error
D. Type I error
1.15 The use of the laws of probability to make inferences and draw statistical
conclusions about populations based on sample data is referred to as ____
[2]
A. Descriptive statistics
B. Inferential statistics
C. Sample statistics
D. Population statistics
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QUESTION 2 [25 MARKS]
2.1 The amounts of electricity bills for all households in a particular city have an
approximately normal distribution with a mean of $140 and a standard deviation of
$30. Find the probability that the mean amount of electricity bills for a random sample
of 75 households selected from this city will be between $132 and $136. [5]
2.2 A study is being made to estimate the proportion of voters in a community who favour
the construction of a nuclear power plant. Determine the sample size necessary to
estimate the population proportion within 0.04 margin of error with 95% confidence,
assuming that a pilot sample gave a proportion of 45%.
[4]
2.3 A random sample of employees of a large company was asked the question, "Do you
participate in the company's stock purchase plan?" The answers are shown below.
Yes No
No
Yes No
No
Yes Yes No
No
No
Yes Yes Yes Yes Yes No
No
Yes Yes
No
Yes Yes No
Yes Yes No
Yes Yes Yes
Use a 99% confidence interval to estimate the proportion of all employees who do
not participate in the company's stock purchase plan.
[5]
2.4 Fifteen Smart Cars were randomly selected in Windhoek and the highway speed of
each was noted. The analysis yielded a mean of 47 kilometres per hour and a standard
deviation of 5 kilometres. Find and interpret a 90% confidence interval for the average
highway speed of all Smart Cars in Windhoek.
[5]
2.5 The IQ test results for BBS112S students are known to be normally distributed.
Suppose a sample of 30 BBS112S students is given an IQ test. If the sample has a
standard deviation of 12.23 points, find and interpret a 95% confidence interval for
the population variance.
[6]
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QUESTION 3 [19 MARKS]
3.1 A manufacturer claims that the thickness of the spearmint gum it produces is 7.50
one-hundredths of an inch. A quality control specialist regularly checks this claim. On
one production run, she took a random sample of n = 10 pieces of gum and measured
their thickness. She obtained:
7.65
7.60
7.65
7.70
7.55
7.55
7.40
7.40
7.50
7.50
Using the above data obtained by the quality control specialist, test the
manufacturer's claim at 5% level of significance.
[8]
3.2 A sample of 314 BBS112Sstudents was askedif they have ever taken an online course.Their
genders were also recorded. The contingency table below was constructed. Use a chi-square
test of independence at 1% of significance to determine if there is a relationship between
gender and whether or not someone hastaken an online course.
(11]
Gender
Men
Women
Have you taken an online course?
Yes
No
43
63
95
113
QUESTIONSTION 4 [26 MARKS]
4.1 The data in the table below present the production of steel (in million tons) in the
Africa 1994-2003.
Year
Production
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
20 22 30 28 32 25 29 35 40 32
4.1.1 Calculate a 3-yearly moving average trend for the time series.
[8]
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4.1.2 Compute the estimated straight line trend equation (Y =a+ bX) by the method of least
squares using the sequential coding method, start the coding from 0 (x=0 for 1994)
[10]
4.1.3 Estimate the production of steel in million tons for the year 2008.
[2]
4.2 By using the data in the table below, calculate and interpret the Laspeyres price index
for 1988 using 1985 as base year.
[6]
Product
A
B
C
1985
Price (N$)
Quantity
1.00
50
0.70
100
0.30
97
1988
Price (N$)
Quantity
1.25
48
0.85
110
0.48
120
=============END OF EXAMINATION===========
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®
®
c.,s.1 for::= J:34,n:fcrioI.he 1.3
ro11:.i•nd!he0.().lcolumn IQ
fil)J,J~cumulath-cruta.0.0901.
The StandardNormalDistribution
c.t~fCK:.,,.1.34.tcftrlothc
l.J rowWldthcll.(};Irolumnto
_&_
The StandardNormalDistribution
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
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
0.5793 0 5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
u
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
-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 00174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
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
u
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
®
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
®
@)
LI
0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0 8770 0,8790 0.8810 0.8830
®
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
u
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
-1.6 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
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
u
0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
u
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 01093 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
u
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
0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
-0.9 0.1841
-0.8 0.2119
-0.7 0.2420
-0.6 0.2743
-0.5 0.3085
-0.4 0.3446
-0.3 0.3821
-0.2 0.4207
-0.1 0.4602
-o.o 0.5000
0.1814
0.2090
0.2389
0.2709
0.3050
0.3409
0.3783
0.4168
0.4562
0.4960
0.1788
0.2061
0.2358
0.2676
0.3015
0.3372
0.3745
0.4129
0.4522
0.4920
0.1762
0 2033
0.2327
0.2643
0.2981
0.3336
0.3707
04090
0.4483
0.4880
0.1736
0.2005
0.2296
0.2611
0.2946
0.3300
0.3669
0.4052
0.4443
0.4840
0.1711
0.1977
0.2266
0.2578
0.2912
0.3264
0.3632
0.4013
0.4404
0.4801
0.1685
0.1949
0.2236
0.2546
0.2877
0.3228
0.3594
0.3974
0.4364
0.4761
0.1660
0.1922
0.2206
0.2514
0.2843
0.3192
0.3557
0.3936
0.4325
0.4721
0.1635
0.1894
0.2177
0.2483
0.2810
0.3156
0.3520
0.3897
0.4286
0.4681
0.1611
0.1867
0.2148
0.2451
0.2776
0.3121
0.3483
0.3859
0.4247
0.4641
0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
u
0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
ll
0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
u
0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
u
0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
u
0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
u
0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
u
0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
u
0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
u
0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
Source. Cumu~111YCi.1and.J1dnotmal p,~1!,t~
gcot'fi!ted tr, M1n,111b.then roundC'<l10 lour dt<1m.ll pl.Kn.
l ~17X_IBC.lndd I
®
a.~PMI GU)2/10
5217X_IBC.ndd 2
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8.~PMI Dtt02/10
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APPENDIX D: The t-distribution
:,//.,
df\\p
0.40
J!o:324920
2 i0.288675
3 i[o.276671
4 • 0.270722
5
6 ,.0.264835
1 .J:o:263167
8 · 0.261921
9 ::0.260955
10 ;,0.260185
11 !:o.2~9556
12 : o.259033
13 "0.258591
14 :·0.258213
15 jio.25iaa5
16 :'0.257599
17 i:0.257347
rn '"0.251123
19
20
21 ''o.256580
22 i'0.256432
23 i'o.256297
24 ,_,J0.256173
25 "0.256060
26
o.255955
27 0.255858
28
29 l!0.255684
30 Jo:25?~~5
in£ ·1:0.253347
0.25
0.10
0.05
).000000 !:3.077684 ;,6.313752
•0.816497 i:l.885618 2.919986 4.30265
0.764892 il.637744 2.353363 3.18245
:o.740697 ).533206 2.131847 2.77645
'1.475884 ).015048 ·2.57058
:0.117558 il.4~9756
.0.711142 ,:1.414924
:1.943180
1.894579
2.44691
2.36462
0.706387 ''1.396815 "l.859548 2.30600
0.102122 }i~3o;~·
.1.833113 2.26216
o.699812 "1.312184 ··1.012451 2.22814
_0.697445
,>:iiss4!i:i
0.693829 '.:1.350171 '1.770933 2.16037
0.692417 !•l.345030 :1.761310 . 2.14479
o.691197 ii1.340606 1.753050 2.13145
.0.690132 l'l.336757
0.689195 l'!.333379
0.688364 ' 1.330391
0.68162.1
!·l.3~7-128....
''1.729133
,,
'o.686954 1'1.325341 l.724718
·o.6863~;·· [:1.323188 i'I.720743
!'2.09302
2.08596
; 2.07961
:o.685805_ ;u21237
:o.685306 [•1.319460
'.0.684850 !'1.317836
·o.684430 \\11.316345
·o.684043 '1.314972
:J.717144 . (1.07387
:1.713872 : 2.06866
;1.710882 . 2.06390
'.J.708141 ' 2.05954
',l.705618 2.05553
0.683685 1.313703 .'J.703288
,.
0.683353 . 1.312527 l.701131
2.05183
'0.683044 'J:i.311434
. !,
0.682756 ''1.310415
"""if'"'"~••••u.,,
·••• ••
'0.674490 ,.l.281552
·.l.699127
l.697261
'2.04227
31.82052
6.96456
0.005 ... i ..0:~~~5
, 63.65674 ;!636.6192
i9.92484 i!3l.5991
. 4.54070 i 5.84091
.3.74695 }4,60409
:,3.36493
·3.14267
; 4.03214
! 3.70743
·2.99795 i 3.49948
2.89646 .._. "i"3{·.3·•5•539
·•2.82144 i 3.24984
if4.5869
':4.4370
2.68100 '3.05454 '<4.3178
:2.65031 3.01228 [4.2208
.2.62449 i 2.97684 [4.1405
2.60248 2.94671 if4,0728
2.92078 !4.0150
2.89823 ,[3.9651
2.87844 !3.9216
,2.53948 2.86093 [3.8834
2.52798 2.84534 ''3.8495
·2.51765
'2,50832
'2.49987 2.80734 '3.7676
2.49216 i 2.79694 ..... J3.7454
2.48511 2.78744 ''3.7251
·:2.47863
,2.47266
2.77871
i 2.77068
·2.46714 2.76326
. 2.46202 2.75639 i3.6594
'.2.45726 2.75000 "3.6460
2.32635 2.57583 ::3.2905
APPENDIX E: The Chi-Square Distribution
·,
I,: . '
.... .,_:
.f1~ ~· -· .,' .
,}
;,1
:d~pJ.995
io.00004
·:0.01003
.975
.i[~.00098
[0.02010 o.o5o64
i! .950
·''·
':0.00393 i:0.01579
i:0.10259 i'o.21012
i!0.10153 i 0.45494 1'1,32330
! ;:o.57536 1.38629 ,
.005
'5.02389 '6.63490 ,'7.87944
·7.37776 I 9.21034 .10.59663
:fo21sso "o.35185 , 058437 Ji:2i2s3
2.36597 -,i 4--.10834
i 3.35669.: 5.38527
6.25139 7.81473
l 7.77944 9.48773 '11.14329 )3.27670 i14.86026
]0.83121 ,;1.14548 ![1.61031 i2.67460 ; 4.35146 i,6.62568 '9.23636 i I 1.07050. :12.83:i°So·:1· s:oe627. ;;-6,74960
:•:i:.-545.0 a123.734 ':1_.63538 ):2.20413
;\\i::i4ei'i , 7.84080 10.64464. 12.s9159 1444938 ,:iG:iiiiiiii. 18.54758
'io.90926 1.23904 i!.1:68987 'i2.16735. "2.03311 '!4.25485 ) 6.34se1 : 9.03115 . 12.01104' 14.06114.}6.01216 10.47531 '20.21114
:,1.34441 :!1.64650
·'s.01o:ii i ; 3.48954
7.34412 ; 10.21885 13.36157 :15.so131 ·,17.53455 ::20.09024 :21.95495
9 '1.13493 :2.00790
10 !2.15586 ·:2.55821
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