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Math 341: Sampling Methods 1 Question Paper
Math 341: Sampling Methods 1
Course:Bachelor Of Science Economics And Statistics
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
THIRD YEAR EXAMINATIONS FOR THE AWARD OF DEGREE OF
BACHELOR OF SCIENCE ECONOMICS AND STATISTICS AND BACHELOR OF EDUCATION
MATH 341: SAMPLING METHODS 1
STREAMS: BSC. ECON &STAT / B.EDUC Y3S2 TIME: 2 HOURS
DAY/DATE: WEDNESDAY 24/4/2013 8.30 AM – 10.30 AM
INSTRUCTIONS:
Answer question 1 and any other two
All working must be clearly shown
Do not write on the question paper
QUESTION 1 (30 MARKS)
(a) Distinguish the following terms as used in sampling methods.
(i) Sampling frame and sampling design
(ii) Unbiased estimator and efficient estimator. [6 Marks]
(b) Define sampling and non-sampling errors and give two sources of each category. [4 Marks]
(c) Prove that in the simple random sampling without replacement, the probability of
selecting a specified unit of the population at any draw is equal to the probability of it being selected at the first draw. [5 Marks]
(d) A random sample of 10 unpaid salary claims was drawn from records at a certain ministry which had a total of 350 unpaid salary claims. The objective was to estimate the amount of money owed by the ministry. The sample values for the amount owed was obtained in Kenya shillings as follows:
3220 240 310 1700 1090
570 2390 690 130 1840
(i) Estimate the population mean. [2 Marks]
(ii) Find 95% confidence interval for the population mean. [3 Marks]
(e) (i) Give two merits and two demerits of systematic sampling. [5 Marks]
(ii) Describe the procedure of stratified random sampling. Under what condition is
stratified random sampling preferred to simple random sampling? [5 Marks]
QUESTION 2 (20 MARKS)
(a) A national park has been divided into 100 tones. A survey is taken with the aim of obtaining the number of Rhinos in the park. Suppose that 40% of the 100 tones are assumed to be inhabited by Rhinos and each zone is assumed to be large.
(i) How large a sample of the 100 tones should be selected in order to obtain an estimate of the population proportion of occupied tones to within 5% of the true proportion with 95% confidence. [6 Marks]
(ii) How large a sample is required if the estimate is to be 5% of the true value with 95% confidence? [4 Marks]
(b) Suppose that an amount c’ has been budgeted for in carrying out a survey. Assuming that the simplest c cost function is c’=co+nG, where Co is the overhead cost and c, the cost of surveying a single unit show that v((??^2)/c_1 ) under SRSWR, and ? is constant.
[10 Marks]
QUESTION 3 (20 MARKS]
(a) A population of size 800 is divided into 3 strata. Their sizes, means and variances are
given below:
Stratum No. Size, Ni Variance S2i
1 200 36
2 300 64
3 300 144
A stratified sample of size 120 is to be drawn without replacement from the population.
Determine the sample size required in case of proportional allocation and Neyman’s optimum allocation. [8 Marks]
(b) Using sample analogue technique or any other technique show that the finite population variance is S2 (i.e E(s^2 )=s^2 ) [12 Marks]
QUESTION 4 (20 MARKS)
(a) Consider a population consisting of 7 units and systematic sample of size 3 is required, where k=7/3=21/3 (i.e 2 or 3). for the case when k = 2,and k=3 show under the circular systematic sampling technique that the systematic sample mean is an unbiased estimator of the population mean. [12 Marks]
(b) A simple random sample without replacement of n = 50 was drawn from a village in which there are N = 500 households. It was found that amongst the sampled households, there are only households each possessing a transistor radio.
(i) Estimate the total number of households in the village possessing transistor
radios. [5 Marks]
(ii) Calculate the standard error of the estimate . [3 Marks]
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