Paper – I : Research Methodology, Sampling Techniques and Statistical Quality Control,2010Question Paper,University Of Pune Question Paper,S.Y.B.A. Examination, 2010

University Of Pune Question Paper
S.Y.B.A. Examination, 2010
STATISTICS (General)
Paper – I : Research Methodology, Sampling Techniques and Statistical
Quality Control
(New Course)
Time : 3 Hours Max. Marks : 80
N.B. : i) All questions are compulsory.
ii) Figures to the right indicate full marks.
iii) Use of statistical table and calculator is allowed.
iv) Symbols and abbreviations have their usual meanings.
v) Graph papers will be supplied on request.
1. Attempt any two of the following : (2×5=10)
a) In SRSWOR, show that the probability of getting a specified rth unit in a
given jth draw is same as the probability of getting that unit in the first draw
itself. Hence find the probability of inclusion of a specified unit in a sample of
size n from a finite population of size N.
b) Discuss, in brief, the need for stratified random sampling. Is the mean of the
stratified random sample unbiased estimator of the population mean ? Justify
your answer.
c) From a population of 500 units, a sample is to be selected by SRSWOR to
estimate the population mean X within 10% of its true value apart from 1 in
20. If the population coefficient of variation is 45%, determine the size of the
sample.
d) Write a note on OC curve of a single sampling plan.
2. Attempt any four of the following : (4×5=20)
a) In stratified random sampling, show that v x( ) st is minimum for fixed cost,
∑=
+=
k
1i
o i i C cC n if
i C
i
i S Ni n α . Also interpret it.
P.T.O.
[3801] – 279 -2-
b) Explain the method of systematic sampling. Give one real life situation where
it can be used.
c) Describe the method of construction of X -chart and R-chart while studying
control chart for variable.
d) State the ratio estimate and regression estimate of the population mean and
population total.
e) For a single sampling plan n = 10, and c= 2. Compute producers risk if
AQL = 5%.
f) In single sampling plan N = 750, n = 76, c = 1 assuming all the lots submitted
are 0.5% defective. Compute AOQ and ATI.
3. Attempt any three of the following : (3×10=30)
a) i) Determine the sample size under SRSWOR of a variable of continuous
type for a given margin of error and confidence coefficient.
ii) Enumerate the salient features of a good questionnaire.
b) Twenty three samples of size 4 each were inspected for a quality characteristic
X. It was found that mean of sample means X is 0.43 and mean of sample
ranges R is 0.01.
i) Compute control limits for X -chart and R-chart.
ii) If the process average shifts to 0.435, what would be the probability of
catching this shift on the second sample taken after the shift ?
c) For the double sampling plan N = 1000, n1 = 50, n2 = 50, c1 = 1, c2 = 2.
Compute ASN and ATI if P = 0.01.
d) With usual notations, prove that v )x(v)x(v)x( . st A.D ≤ st A.P ≤ SRSWOR
e) Explain the construction of p-chart by using :
i) Varying control limits
ii) Average sample size.
4. Attempt any one of the following : (1×20=20)
a) A sample of 60 students drawn from a population of size 600 students
belonging to three colleges. The following information was collected about
certain characteristic.
Stratum Total No.
of students
Sample
mean
Sample
mean square
College I 250 30 64
College II 250 25 81
College III 100 20 121
i) Obtain P.A. and N.A. for n = 60
ii) Estimate the population mean and the variance of thisestimator.
b) i) What is the meaning of ‘Research’ ? State various types of research.
ii) Distinguish between ‘Ratio Scale’ and ‘Interval Scale’. In which situation
Likert scale is used ?
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