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BBS112S- BASIC BUSINESS STATISTICS 1B- JAN 2020 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
Faculty of Health and Applied Sciences
Department of Mathematics and Statistics
QUALIFICATIONS: B. Business Admin, B. Marketing, B. Human
Management and B. Logistics and Supply Chain Management
QUALIFICATION CODES: 21BBAD / 07BMAR/ LEVEL: 6
O7B/ H24R BPN / 07BLSM
,
Resource
Management,
COURSE: BASIC BUSINESS STATISTICS 1B
COURSE CODE: BBS112S
B. Public
DATE: JANUARY 2020
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
SECOND
EXAMINER(S)
OPPORTUNITY/SUPPLEMENTARY EXAMINATION QUESTION PAPER
MR EM MWAHI, MS A SAKARIA, MR | NDADI, MR G MBOKOMA, MRR MUMBUU,
MR A ROUX, MR G TAPEDZESA
MODERATOR:
MR JJ 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, Student t-table and Chi-square table.
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QUESTION 1 [30 MARKS]
1.1
If true value of population parameter is 10 and estimated value of population
parameter is 15 then error of estimation is:
[2]
A.5
B. 25
c.1.5
D. 0.667
1.2 Parameters and statistics...
[2]
A.
Are both used to make inferences about the sample mean.
B.
Describe the population and the sample, respectively.
C.
Describe the sample and the population, respectively.
D.
Describe the same group of individuals.
1.3 What should be the critical value of z used in a 93% confidence interval?
[2] *
A. 2.70
B. 1.40
Cc. 1.81
D. 1.89
1.4 Arandom sample of 100 observations is to be drawn from a population with a mean
of 40 and a standard deviation of 25. The probability that the mean of the sample
will exceed 45 is?
[2]
A. 0.477
B. 0.4207
C. 0.0793
D. 0.0228
1.5 Suppose we sample by selecting every fifth invoice in a file after randomly obtaining
a starting point. What type of sampling is this?
[2]
A. Simple random sampling.
B. Cluster random sampling.
C. Stratifies random sampling.
D. Systematic random sampling.
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1.6 A 95% confidence interval for a population mean is determined to be 100 to 120. If
the confidence level is reduced to 90%, the interval:
[2]
A. Becomes narrower.
B. Becomes wider.
C. Does not change.
D. Becomes 0.1.
1.7 An interval estimate is a range of values used to estimate:
[2]
A. The shape of the population's distribution.
B. The sampling distribution.
C. Asample statistic.
D. A population parameter.
1.8 Suppose that we wanted to estimate the true average number of eggs a queen bee
lays with 95% confidence. The margin of error we are willing to accept is 0.5.
Suppose we also know that the population standard deviation is 10. What sample
size should we use?
[2]
A. 1536
B. 1537
C. 2653
D. 2650
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 The form of the alternative hypothesis can be:
[2]
A. one-tailed
B. two-tailed
C. neither one nor two-tailed
D. one or two-tailed
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1.11 Which of the following is true of the null and alternative hypotheses?
[2]
A. Exactly one hypothesis must be true
B. both hypotheses must be true
C. It is possible for both hypotheses to be true
D. It is possible for neither hypothesis to be true
1.12 A type Il error occurs when:
[2]
A. the null hypothesis is incorrectly accepted when it is false
B. the null hypothesis is incorrectly rejected when it is true
C. the sample mean differs from the population mean
D. the test is biased
1.13 Test of hypothesis Ho: 1 = 50 against H1: p > 50 leads to:
[2]
A. Left-tailed test
B. Right-tailed test
C. Two-tailed test
D. Difficult to tell
1.14 When ois known, the hypothesis about population mean is tested by:
[2]
A. t-test
B. Z-test
C. x2-test
D. F-test
1.15 The purpose of statistical inference is:
[2]
A. To collect sample data and use them to formulate hypotheses about a population
B. To draw conclusion about populations and then collect sample data to support the
conclusions
C. To draw conclusions about populations from sample data
D. To draw conclusions about the known value of population parameter
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QUESTION 2 [25 MARKS]
Zak 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 mean thickness of the spearmint gum it produces is
7.50 one-hundredths of aninch. 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 BBS112S students was asked if 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 has taken 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 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.
[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 (NS)
Quantity
1.00
50
0.70
100
0.30
97
1988
Price (NS)
Quantity
1.25
48
0.85
110
0.48
120
S=S==========END OF EXAMINATION========2=2=
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e.g., for z= —1.34, refer to the — 13
row and the 0.04 column to
find the cumulative area, 0.0901.
The Standard Normal Distribution
z
0.00
-3.0 0.0013
-2.9 0.0019
-2.8 0.0026
-2.7. 0.0035
-2.6 0.0047
-2.5 0.0062
-2.4 0.0082
-2.3 0.0107
-2.2 0.0139
-2.1 0.0179
—2.0 0.0228
-1.9 0.0287
-1.8 0.0359
-1.7 0.0446
-16 0.0548
-1.5 0.0668
-1.4 0.0808
-1.3 0.0968
—1.2 0.1151
-1.1 0.1357
-1.0 0.1587
-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
-0.0 0.5000
0.01
0.0013
0.0018
0.0025
0.0034
0.0045
0.0060
0.0080
0.0104
0.0136
0.0174
0.0222
0.0281
0.0351
0.0436
0.0537
0.0655
0.0793
0.0951
0.1131
0.1335
0.1562
0.1814
0.2090
0.2389
0.2709
0.3050
0.3409
0.3783
0.4168
0.4562
0.4960
0.02
0.0013
0.0018
0.0024
0.0033
0.0044
0.0059
0.0078
0.0102
0.0132
0.0170
0.0217
0.0274
0.0344
0.0427
0.0526
0.0643
0.0778
0.0934
0.1112
0.1314
0.1539
0.1788
0.2061
0.2358
0.2676
0.3015
0.3372
0.3745
0.4129
0.4522
0.4920
0.03
0.0012
0.0017
0.0023
0.0032
0.0043
0.0057
0.0075
0.0099
0.0129
0.0166
0.0212
0.0268
0.0336
0.0418
0.0516
0.0630
0.0764
0.0918
0.1093
0.1292
0.1515
0.1762
0.2033
0.2327
0.2643
0.2981
0.3336
0.3707
0.4090
0.4483
0.4880
0.04
0.0012
0.0016
0.0023
0.0031
0.0041
0.0055
0.0073
0.0096
0.0125
0.0162
0.0207
0.0262
0.0329
0.0409
0.0505
0.0618
0.0749
0.0901
0.1075
0.1271
0.1492
0.1736
0.2005
0.2296
0.2611
0.2946
0.3300
0.3669
0.4052
0.4443
0.4840
0.05
0.0011
0.0016
0.0022
0.0030
0.0040
0.0054
0.0071
0.0094
0.0122
0.0158
0.0202
0.0256
0.0322
0.0401
0.0495
0.0606
0.0735
0.0885
0.1056
0.1251
0.1469
0.1711
0.1977
0.2266
0.2578
0.2912
0.3264
0.3632
0.4013
0.4404
0.4801
0.06
0.0011
0.0015
0.0021
0.0029
0.0039
0.0052
0.0069
0.0091
0.0119
0.0154
0.0197
0.0250
0.0314
0.0392
0.0485
0.0594
0.0721
0.0869
0.1038
0.1230
0.1446
0.1685
0.1949
0.2236
0.2546
0.2877
0.3228
0.3594
0.3974
0.4364
0.4761
0.07
0.0011
0.0015
0.0021
0.0028
0.0038
0.0051
0.0068
0.0089
0.0116
0.0150
0.0192
0.0244
0.0307
0.0384
0.0475
0.0582
0.0708
0.0853
0.1020
0.1210
0.1423
0.1660
0.1922
0.2206
0.2514
0.2843
0.3192
0.3557
0.3936
0.4325
0.4721
0.08
0.0010
0.0014
0.0020
0.0027
0.0037
0.0049
0.0066
0.0087
0.0113
0.0146
0.0188
0.0239
0.0301
0.0375
0.0465
0.0571
0.0694
0.0838
0.1003
0.1190
0.1401
0.1635
0.1894
0.2177
0.2483
0.2810
0.3156
0.3520
0.3897
0.4286
0.4681
0.09
0.0010
0.0014
0.0019
0.0026
0.0036
0.0048
0.0064
0.0084
0.0110
0.0143
0.0183
0.0233
0.0294
0.0367
0.0455
0.0559
0.0681
0.0823
0.0985
0.1170
0.1379
0.1611
0.1867
0.2148
0.2451
0.2776
0.3121
0.3483
0.3859
0.4247
0.4641
Source: Cumulative standard normal probabilities generated by Minitab, then rounded to four decimal places.
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1.9 Page 9 |
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e.g., for z = 1.34, refer to the
1,3 row and the 0.04 column to
! find the cumulative area, 0.9099.
The Standard Normal Distribution
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
1.000000
0.816497
764892
740697
533206 2.131847
T5884
264835 0.717558
“1.943180
0.263167 0.711142, 414924 1.894579
0.261921
0.260955
0.260185
0.706387_ 396815)
"0.702722 / 1.383029
0.699812 “1.372184
1.859548
1.812461
0.259556 "0.697445
0.259033 0.695483
1.782288
0.258591 0.693829
1.770933 2.16037
0.258213 0.692417
1.761310 "2.14479
0.691197 1.340606 "1.753050
0.257599
© 0.257347
0.257123
"0.256923
0.690132
0.689195
0.688364
0.687621
1.336757 “1.745884 2.11991
1.739607 2.10982
1.330391 1.734064
1.327728 1.729133 _
0.256743
/ 0.256580
0.256432
0.256297
0.686954
0.686352
0.685805
0.685306
/1.325341 1.724718
1.321237 | 1.717144
Saeco nee
1.713872
.256173 0.684850 (1.317836 1.710882
0.256060 0.684430
1.708141
0.255955 0.684043
“1.705618
0.255858 (0.683685
(0.255768 ‘0.683353
1.703288 2.05183
1.701131 2.04841
684
.255605
0.253347
0.674490
+ 1.281552
1.697261
+1.644854 1.95996
om aa
31.82052
6.96456
“4.54070
3.74695
3.36493
3.14267
+ 2.99795
2.89646
2.82144
2.76377
"2.71808
2.68100
2.65031
2.62449
2.60248
2.58349
2.56693
"2.55238
2.53948
2.52798
"2.51765
2.50832
2.49987
(2.49216
2.48511
(2.47863
2.47266
2.46714
2.46202
2.45726
2.32635
0.005
0.0005
636.6192
"31.5991
12.9240
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2.1 Page 11 |
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APPENDIX E: The Chi-Square Distribution
995
975 «950
[ 1 | 0.00004
2 0.01003
3 0.07172
0.00098 0.00393
0.05064 0.10259
0.21580 0.35185
4 0.20699
5 0.41174
0.48442 0.71072
| 0.83121 1.14548
:76
0.67573
0.98926
1.63538
8 1.34441
9 1.73493
10) 2.15586
3.24697
11 2.60322
12 3.07382
44
43° 3.56503 4.10692 5.00875
14 4.07467
8.62873
460092
6.26214
5.6
18 6.26480
| 6.90766
6756419
19 6.84397
20 7.43384
“21 8.03365
22 8.64272
9.26042
9.88623
|
750 = «500250
(0.10153 0.45494 1.32330
0.57536 1.38629 2.77259
1.21253
/1,92256
-2.67460
7 17.11693.
-18.24509
(5.02389 6.63490 7.87944
(737776 9.21034
9.34840
| 1.14329 |
| 12,83250__
4.44938
16.0276
-17.53455 20.09024
/ 19.0227 | 21.66599
-35.47888 38.
/36.78071__
“40.64647 | 4.3
4192317 |
(4.46079 4
45.7229