Download SYLLABUS FOR Ph

SYLLABUS FOR Ph.D
QUANTITATIVE TECHNIQUES
Course Code: PST 901
Credit Units: 04
Course Objective:
The aim of this course is to develop the understanding of the various Statistical models and
Optimization Techniques used for analysis of data/information to make final recommendations
in various interdisciplinary domains of research
Course Contents:
Unit 1: Introduction
Nature and Scope of Quantitative Analysis, Developing a Model, Quantifying the Model and
the Solution, Variables and functions – Linear, Quadratic and Exponential functions; Elements of
Calculus – Limits, Continuity and Differentiation.
Unit 2: Application of Statistical tools
Measures of Central tendency – Mean, Median, Mode; Introduction of Probability Theories and
Concepts, Probability Distributions- Discrete and Continuous Probability Distributions;
Measures of Association: Correlation and regression; Advance Multivariate analysis discriminant analysis, cluster analysis, factor analysis and conjoint analysis;
Unit 3: Data Analysis Techniques:
Quantitative and qualitative methods of data analysis; Hypothesis Testing - Parametric tests (Ztest, t-test, F-test) and Non-parametric Tests (Chi-Square Test, ANNOVA), Tests of significance
based on normal distributions; association of attributes; Use of IT software in data analysis and
data presentation; Matlab and SPSS software.
Unit 4: Index Numbers, Forecasting and Time Series Analysis
Uses of Index Numbers; Methods of constructing; Index Numbers; Types and Methods of
forecasting; Steps in forecasting; Time series analysis; Time Series Decomposition.
Unit 5: Optimization Techniques
Introduction of Linear Programming, Formulation and Solution of LPP, PERT and CPM
Examination scheme
Components
Internal
Attendance
End Semester
Weightage
25
5
70
(%)
 Internal Components includes: Case study/ Presentations/ Fieldwork/ Viva voce
 At least two internal components must be included
List of Practicals in Quantatives Techniques
The practicals shall be devoted to using computer / statistical software (SPSS / MATLAB etc.)
for solving the following kind of problems:
Q1. A certain population is divided into 5 strata so that N1=2000,N2=2000,N3=1800,N4=1700
and N5=2500 ,respective standard deviations are 1.6,2,4.4,4.8,6.0 and further the sampling cost
in the first two strata is 4 per interview and the three remaining strata is 6 per interview , how
should a sample of size n=226 be allocated to the 5 strata if we adopt proportionate sampling
design.
Q2. Out of 1,000 patients examined on entry to a hospital, 427 were men and 573 were women.
Anemia is detected in 323 of the men and 375 of women. Test the hypothesis that anemia is
equally frequent in men and women using a chi-square test using SPSS
Q3. Solve the problem in question 2 by testing the null hypothesis that anemia is equally
frequent among both the sexes by using Normal approximation to Binomial distribution you an
use Matlab or SPSS for calculation of result .
Q4. Twenty insects were used in an experiment to examine the effect on their activity level, y, of
3 standard preparations of a chemical. The insects were randomly assigned, 4 to receive each of
the preparations and 8 to remain untreated as controls. Their activity levels were metered from
vibrations in a test chamber and were as follows:
Activity levels (y)
Totals
Control
43 40 65 51 33 39 54 62
387
Preparation A
73 55 61 65
254
Preparation B
84 63 51 72
270
Preparation C
46 91 84 71
292
For these data y1 =1203, y2 = 77249.
(i) Conduct an analysis of variance test to establish whether the data indicate significant
differences amongst the results for the four treatments.
Q5. A new project has 'average' novelty for the software supplier that is going to execute it and is
thus given a 3 rating on this account for precedentedness. Development flexibility is high to the
extent that this generates a zero rating, but requirements may change radically and so the risk
resolution exponent is rated at 4. The team is very cohesive and this generates a rating of 1, but
the software house as a whole tends to be very informal in its standards and procedures and the
process maturity driver has therefore been given a value of 4. What would be the scale factor (sf)
that would be applicable in this case?
Q6. Let Y1,Y2,Y3,Y4,Y5,Y6 and Y7 represent the observed average performances of a group
of 100 Ph.D. Research Scholars in the following subjects Mathematics, Science, English,
Foreign language, Running speed, Strength, Agility and F1 and F2 are unobservable indexes of
intellectual and physical .abilities Explain by writing a model how the factor analysis technique
can be applied to estimate F1 and F2 with an example; given that the first 4 subjects measure
intellectual ability while the last three measure mental ability.
Q7. Calculate the sample mean and standard deviation of the following claim amounts (£):c 534
671 581 620 401 340 980 845 550 690 using SPSS.
Q8.(i) Hemoglobin level of 10 men and 10 women are given as follows:
Men:
14. 0, 14.6, 17.4, 14.4, 15.4, 14.8, 16.1, 15.5, 14.5, 14.3
Women: 12.5, 12.7, 13.1, 12.8, 14.7, 13.5, 13.3, 13.6, 13.2, 14.6
Perform an ANOVA to test whether the means differ in two tests significantly using SPSS or
Matlab
Q9. Fit a Normal distribution model for the following Serum-Iron data and test the goodness of
fit by chi-square test. Mid point of the class interval of length 10:
104.5, 114.5, 124.5, 134.5, 144.5, 154.5, 164.5
Q10. For a group of policies the total number of claims arising in a year is modelled as aPoisson
variable with mean 10. Each claim amount, in units of £100, is independently modelled as a
gamma variable with parameters = 4 and = 1/5.Calculate the mean and standard deviation of the
total claim amount.
Q11 In a survey conducted by a mail order company a random sample of 200 customers yielded
172 who indicated that they were highly satisfied with the delivery time of their orders. Calculate
an approximate 95% confidence interval for the proportion of the company s customers who are
highly satisfied with delivery times.
Q12. The following table gives the numbers of occupants in 2,423 cars observed on a road
junction during a certain time period on a weekday morning.
Number of occupants 1, 2, 3, 4, 5, 6
Frequency of cars 1486, 694, 195, 37, 10, 1
The above data were modeled by a zero-truncated Poisson distribution as given in (i).
The maximum likelihood estimate of is = 0.8925 and the Cramer-Rao lower bound on variance
at = 0.8925 is 5.711574 10 4 (you do not need to verify these results.)
(a) Obtain the expected frequencies for the fitted model, and use a 2 goodness-of-fit test to show
that the model is appropriate for the data.
(b) Calculate an approximate 95% confidence interval for and hence calculate a 95% confidence
interval for the mean of the zero-truncated Poisson distribution.