LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS
FOURTH SEMESTER – APRIL 2007
ST 4200 / 3200 – ADVANCED STATISTICAL METHODS
Date & Time: 25/04/2007 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
PARTA
Answer all the questions. 10×2=20 marks
 Define dichotomous and manifold classification.
 For two attributes A and B if (AB)=20, (Aβ)=25 ,(αB)=32 and N=100 ,find
(A) and (B)
 Write the conditions for the consistency of data for three attributes.
 State the axiomatic definition of probability.
 When do you say that three events A,B and C are independent?
 Define binomial distribution.
 What are TypeI and TypeII errors in testing of hypothesis.
 Write any two applications of chisquare distribution.
 Write a note on chance and assignable causes in quality control.
 State the control limits for p chart.
PARTB
Answer any five questions. 5×8=40 marks
 Can vaccination be regarded as a preventive measure for smallpox from the
data given below?
“Of 1482 persons in a locality exposed to smallpox ,368 in all were attacked.”
“Of 1482 persons ,343 had been vaccinated and of these only 35 were attacked.”
 For n attributes A_{1},A_{2},…A_{n}, show that
(A_{1} A_{2},…A_{n})(A_{1}) + (A_{2}) +…. +(A_{n})(n1)N, where N is the total number of
observations.
 If 10 fair coins were tossed simultaneously, find the probability of getting
(a) atleast 1 head (b) atmost 2 heads (c) exactly 8 heads(d)not more than 4 heads.
 If X is Poisson variate such that
P(X=2)=9 P(X=4) + 90 P(X=6) find mean and variance.
15 (a) If X follows normal distribution with mean show that and variance ^{2 }
then show that (X)/ follows standard normal distribution.
(b) Write any four characteristics of normal distribution.
 A random sample of 10 boys had the following
I.Q’s:70,120,110,101,88,83,95,107,100.
Do these data support the assumption of a population mean I.Q.of 100?
Use 5% level of significance.
 The mean height of 50 male students who showed above average participation in
college athletics was 68.2 inches with a standard deviation of 2.5 inches ;while 50
male students who showed no interest in such participation had a mean height of
67.5 inches with a standard deviation of 2.8 inches.Test the hypothesis that male
students who participate in college athletics are taller than other male students. Use
1% significance level.
18.Draw a c chart for the following number of defects found in welding of seams:
2 4 7 3 1 4 8 9 5 3 7 11 6 4 9 9 6 4 3 9 7 4 7 12. Check whether the
process is in control .
PARTC
Answer any two questions. 2×20 = 40 marks
 (a) Establish the relationship between Yule’s coefficient of association and
coefficient of colligation.
(b) Given the following data find the postive classes:
(ABC) = 148, (AB)=738 (AC)=225 (A)=1196 (BC)=204
(B)=1762 (C)=171 and ()=21842.
(c) Among the adult population of a certain town 50 % are males ,60%are
wage earners and 50% are 45 years of age or over,10%of the males are not
wage earners and 40% of the males are under 45.Make the best possible
inference about the limits within which the percentage of persons(male or
female) of 45 years or over are wage earners .
20.(a). Fit a Poisson distribution to the following data and test for the goodness of fit:
No.of mistakes/ page: 0 1 2 3 4
No. of pages: 109 65 22 3 1
Use 1% significance level.
(b). If X is a normal variate with mean 30 and S.D. 5,find the probability of
(i) 26 ≤ X ≤ 40 (ii) X 45 (iii)X30 >5.
 Analyze the following data at 1% significance level:
Treatments
1 2 3 4 5 6
Blocks
1 24.7 20.6 27.7 16.2 16.2 24.9
2 27.3 28.8 22.9 15.0 17.0 22.5
3 38.5 39.5 36.5 19.6 15.4 26.3
4 28.5 31.0 34.9 14.1 17.7 22.6
22.(a).Consruct a control chart for mean and the range for the following data on the
basis of fuses ,samples of 5 being taken every hour . Comment on whether the
production seems to be under control ,assuming that these are the primary data.
42 42 19 36 42 51 60 18 15 69 64 61
65 45 24 54 51 74 60 20 30 109 90 78
75 68 80 69 57 75 72 27 39 113 93 94
78 72 81 77 59 78 95 42 62 118 109 109
87 90 81 84 78 132 138 60 84 153 112 136
(b).The following are the figures of defectives in 22 lots each containing 2000 rubber
belts: 425,430,216,341,225,322,280,306,337,305,356,402,216,264,126,409
193,326,280,389,451,420.
Draw control chart for fraction defective and comment on the state of control
of the process.
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