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SAT802S - SAMPLING THEORY - 1ST OPP - NOVEMBER 2023 |
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n Am I BI A u n IVER s I TY
OF SCIEnCE TECHnOLOGY
FacultyofHealth,Natural
ResourcesandApplied
Sciences
Schoolof NaturalandApplied
Sciences
Department of Mathematics,
Statisticsand Actuarial Science
13JacksonKaujeuaStreet
PrivateBag13388
WindhOek
NAMIBIA
T: •264 612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION : BACHELOR OF SCIENCE HONOURS IN APPLIED STATISTICS
QUALIFICATION CODE: 08BSSH
COURSE: SAMPLING THEORY
DATE: NOVEMBER 2023
LEVEL: 8
COURSE CODE: SAT802S
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
EXAMINER:
MODERATOR:
FIRST OPPORTUNITY: QUESTION PAPER
Mr Simon Pombili Kashihalwa
Dr Isak Neema
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
This paper consists of 4 pages including this front page
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QUESTION 1 (251
a) Discuss the following concepts as used in sampling theory
(i) Sampling design
[2]
(ii) Quota Sampling
(2)
(iii) Non-probability sampling
(2)
(iv) Snow ball
(2)
(v) Sampling error
[2)
b) Write a short notes on the concepts: Sampling error and Non-sampling error
[4)
c) Discuss why we use the sampling with replacement in sampling theory?
[SJ
d) Briefly discuss three principal reasons for using stratified random sampling rather
than simple random sampling
(6)
Question 2(251
2.1 To estimate the total number of students needed to work on a turn-around strategy, the
Registrar office subdivide the strategy into 100 equally sized units. The observed samples
are given below;
234,256,128,245,211,240,202,267
a) Estimate the population total
[4)
b) Estimate Var(y)
[6]
2.2 A farm has 1000 young pigs with a weight of about 50 lbs (1 pound=0.4Skg). They put
them on a new diet for 3 weeks (minimum weight is estimated to be lOlbs).
a) How many pigs should they sample to estimate the average weight gain, if they
want the answer to be within 2 lbs. with 90% confidence.
(15)
Question 3(501
3.1 NUST knows that 40% of its account receivable comes from student and 60% from
Government (subsidy). An auditor randomly sampled 100 accounts without replacement.
Here are the results of his sampling:
Students
n1 =70
5'1=520
S1=210
Government
n 2=30
5'2=280
S2=90
a) Compute the post-stratified mean and the variance of the post-stratified
(10)
SAMPLING THEORY (SAT802S)
l' t Opportunity November 2023 2
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b) The auditor wants to estimate the proportion of each stratum that pays towards
= = = NUST, if N1 50, N2 60, N3 35, use the table below to answer the following
questions
Stratum
Sample size
sample proportion
Students
20
0.8
Government
8
0.5
Others
12
0.5
( i)
Compute the estimator for the population proportion
[4]
(ii)
Compute the variance for each stratum
[9]
3.2 A mathematics achievement test was given to 486 students prior to entering a certain college
who then took a calculus class. A simple random sampling of 10 students are selected and
their calculus score recorded. It is known that the average achievement test score for the 486
students was 52. Study the following output and ANOVAtable and answer the questions that
follows.
Output
Predictor
Coef
StDev
Cons
40.784
8.507
X
0.7656
0.175
Source
DF
ANOVA
ss
MS
Regression
1
1450
1450
Residual
8
606
75.8
a) Using the results from the output, what do you get for the regression estimate? [4]
b) What is the variance of the regression estimate?
[8]
c) Calculate the 95% Cl for f..L
[8]
d) Find R2
[3]
e) Compute the t-values for each predictor
[2]
f) Compute the F statistics
[2]
END
SAMPLINGTHEORY(SAT802S)
Ft Opportunity November 2023 3
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t Table
cum. prob
one-tail
t.~'J
0.50
two-tails
di
1
2
3
4
5
6
7
8
g
10
11
12
,13~
15
16
H
18
1_9
20
21
22
23
24
25
26
27
28
29
1.00
0.000
D.OClO
0.000
0.000
0.000
0.000
0.000
0.00-0
0.000
0.000
0.000
0.000
0.000
0.000
O.OCO
0.000
0.000
o.oco
0.000
0.000
0.000
O.OCO
0.000
O.OGO
O.OCO
0.000
0.000
0.000
0.000
f .JB
0.25
0.50
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703
0.700
0.697
0.695
0.694
0.692
0.691
0.690
0.689
0.668
0.688
0.687
0.666
0.686
0.685
0.685
0.664
0.684
0.664
0.683
0.683
t_..,
{"'~
0.20
0.15
0.40 0.30
1.376
1.061
0.976
0.9,:i
0.920
0.906
0.696
0.689
0.883
0.679
C.676
0.873
0.870
0.868
C'.666
0.865
0.863
0.662
0.861
0.8€0
iJ.659
0.855
rJ.S!:E-
0.857
0.85'5
0.656
0.855
0.855
0.654
1.%3
i.3¢6
1.250
l.190
;_ 156
1.134
1.119
1.108
1.100
1.093
,.ass
1.CB3
1.C,79
1.076
1.0'74
1.071
1.069
l.C67
1.066
1.()64-
1.()63
i.C61
1.C60
1.C59
l.C58
1.058
3.057
1.056
1.055
r_,.,
0.10
0.20
I.,
0.05
0.1.0
t ,'!f:r.
0.025
0.05
3.078
1.836
1.638
1.533
1.476
1-440
1.415
1.397
1.383
1.3n
1.363
1.350
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.3iS
1.316
1.315
1.31-l
1.313
1.311
6.314
2.920
2.353
2.132
2.015
t.943
1.895
1.860
1.833
1.812
1.796
1.762
t.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.7D8
1.706
1.703
1.701
1.699
12.71
4.303
3.182
2.776
2.571
2.447
2.365
2.308
2262
2.228
2201
2.179
2.160
2.145
2.i31
2.120
2.110
2.101
2.093
2!1)86
2.080
2.074
2.069
2,06'!
2.060
2.056
2.052
2.048
2.045
1 ...
0.01
0.0 21
31.82
6.965
4.5':1
3.7t.7
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2..583
2.567
2.552
2.539
2.528
2.518
2.506
2.500
2.492
2.485
2.479
2.473
2.467
2.462
t_.,,=,
0.005
0.01
I·""'
0.001
0.002
[_fllJ~
o.00051
0.001
63.66
9.925
5.B41
4.60-<:
4.032
3.707
3.499
3.355
3.250
3.169
3.i06
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.631
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
318.31
22.327
10.215
7.173
5.89•3
5208
4.735
4.501
4.297
4.144
4.025
3.930
3.S52
3.787
3.73.3
3.686
3.646
3.610
3.57'9
3.SS2
3.527
3.5()5
3.485
3.467
3.450
3.435
3.421
3.408
3.396
636.62
31.599
12.924
8.610
6.869
5.959
5.408
5.041
4.781
4.587
4.~37
4.318
4.221
4.140
4.073
4.015
3.965
3.922
3.8S3
3.!I50
3.819
3.792
3.768
3.745
3.725
3.707
3.6'90
3.674
3.659
SAMPLING THEORY (SAT8025}
l'tOpportunity November 2023 4