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Sample Survey Question Paper
Sample Survey
Course:Bachelor Of Economics
Institution: Kenyatta University question papers
Exam Year:2010
KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
ARTS AND BACHELOR OF ECONOMICS
AEC 404:
SAMPLE SURVEY
DATE: Tuesday, 29th December, 2009
TIME: 4.30 p.m. ? 6.30 p.m.
------------------------------------------------------------------------------------------------------------
INSTRUCTIONS:
Answer question ONE and any other TWO questions.
Q.1
a)
Number of items produced by 3 machines A, B and C are 300, 200 and
500 respectively. Draw a proportional stratified sample of size 20 using
the following random numbers starting from first row.
41206
53802
76310
94283
11245
12638
91165
19152
11143
12583
39276
05284
00135
28105
90312
11390
02487
03001
89001
66530
(8 marks)
b)
Airline ?A? took a simple random sample of 5000 of the 100,000 tickets
purchased from it (on ach ticket, the passenger was carried by both airline
?A? and airline ?B?). The amount X that airline ?A? owed ?B? on each
ticket was calculated and all 5000 were summarized with
X =
2
.
53 and S = 108.
Stratification according to the total cost T of the ticket gave further details.
Page 1 of 5
Stratum Population
Prespecified Sample
Frequency
Size
X
S1
1
0 < T < 100
50,000
2500
15
35
100 < T ? 250
20,000
1000
29
62
250 < T ? 500
20,000
1000
63
75
500 < T
10,000
500
246
164
100,000
i)
Calculate the total amount owed B including 95% confidence interval
(7 marks)
Suppose the large tickets were more expensive to process ? the cost for a ticket in
stratum 1, 2, 3 and 4 averaged out to be $25, $36 and $64 and $100 respectively.
ii)
What was the cost of the stratified sampling?
(5 marks)
iii)
For the same cost, what would the sample size be if optimal stratified sampling
were used?
(6 marks)
iv)
How much would the optimal design reduce the uncertainty (SE) of the estimate?
(4 marks)
Q.2
a)
The following are the numbers of departmental stores 35, 27, 24, 32, 42,
30, 34, 40, 29 and 28. If we want to select a sample of 15 stores using
cities as clusters and selecting within clusters proportional to size, how
many stores from each city should be chosen? (Use a starting of 4)
(6 marks)
b)
An advertising agent for a firm that sells households products wishes to
estimate the monthly expenditures on magazines and newspapers by the
households of certain Midwestern city to determine whether such
expenditures are sufficient to warrant the use of these media sample
sources for advertising. A simple random sample of 10 precincts is
selected from the 50 precincts within the city. Interviewers then survey
Page 2 of 5
every household within the 10 precincts and record the total household
expenditure on magazines and newspapers during the post month.
Sample No.
of
Total
Sample No.
of Total
Households Expenditure
Household Expenditure
1 62
380
6
69
403
2 55
517
7
58
535
3 49
480
8
74
486
4 71
613
9
57
450
5 70
5401
10
65
395
i)
Estimate the average monthly household expenditure on magazines and
newspaper in the city and place a bound on the error of estimation.
(7 marks)
ii)
Estimate the total monthly expenditures on magazines and newspapers by
all the households in the city and place a bound on the error of estimation.
(7 marks)
Q.3
a)
The dean of a business school is considering canvassing the members of
the schools alumni association for the purpose of generosity donations to
the schools development fund. Currently there are 3500 members of the
alumni association, 2100 of whom live in state while the remainder lives
out-of-state. The dean has decided to select a stratified sample of alumni
(stratified according to current residence) to estimate total donations, and
using sample evidence, he will decide whether to contact all remaining
alumni.
i)
Find the number of alumni that should be contacted if the dean
wishes to estimate the total alumni contributions with a bound on
the error of estimation of 10,000.
(5 marks)
Page 3 of 5
ii)
How should this sample size be allocated between in-state and out
of state alumni? From prior fund-rising drives the standard
deviations for donations by in-state and out-of-state alumni were
found to be 30 and 20 respectively.
(7 marks)
b)
A population is divided into three strata so that N1 = 5000, N2 = 2000 and
N3 = 3000 respectively. Standard deviations are ? = ,
15 ? = ,
18 and ? =5 .
1
2
3
How should a sample of size n = 84 be allocated to the three strata.
If you want optimum allocation and using disproportionate sampling
designs.
(8 marks)
Q.4
a)
Outline the step-by-step procedure you would utilize to select the
following:
i)
A sample of 150 students at your university.
(3 marks)
ii)
A sample of 50 light users and 50 heavy users of beer in a
shopping mall intercept sample.
(3 marks)
iii)
A sample of 50 mechanic engineers, 40 electrical engineers and 40
civil engineers from the subscriber list of an engineering journal.
(3 marks)
iv)
A sample of banks, saving and loans, and other financiers of home
mortgage
loans. (3
marks)
b)
Discuss the advantages of conducting a sample survey instead of a census
in each of the following instances.
i)
A candidate for governor of the state of Arizona wishes to know
the proportion of Arizona voters favouring his candidacy one week
prior
to
the
election.
(2
marks)
ii)
A
market
representative
for
a
breakfast food company is interested
in determining the total first year sales of a new package breakfast
food the company has developed.
(2 marks)
iii)
A local newspaper has adopted a more liberal new editorial policy.
To obtain reader reaction to this change, an agent for the
newspaper randomly selects 10 local subscribers from a
Page 4 of 5
subscription list, contact them by phone, and ask them for the
opinion of the change in editorial policy.
(2 marks)
iv)
To determine the proportion of residents favouring a municipal
bond levy, the city manager proposes selecting every 25th
individual listed in the city telephone directory and obtaining his of
her opinion by a telephone poll.
(2 marks)
Q.5
a)
A newspaper has 39,800 subscribers served by carriers routes. There is a
card for subscribers. In the face of the cards of each carrier route are kept
together in geographical order and neighboring routes follow each other.
The chief purpose of the survey is to find out how many of the subscribers
own their homes.
Suppose a systematic sample of n = 30 element of a population result in
the following sample presented in the order they were drawn
9,10,8,9,9,4,5,0,4,7,6,10,4,4,8,9,10,10,7,5,3,2,1,8,9,10,9,8,9,10
Required:
i)
Calculate the mean of the sample
(4 marks)
ii)
Using both successive and paired selections compute the variance
(6 marks)
iii)
Estimate total number of subscribers who own their houses
(4 marks)
b)
A population consists of N = 960 elements which can be numbered
consecutively. The required sample size n = 60. Select 10 repeated
systematic samples in place of the one systematic, if random stating point
is
73,42,81,145,6,21,86,17,112,102
(6
marks)
Page 5 of 5
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