LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

 AC 10

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

PART-A

Answer all the questions.                                                                            10×2=20 marks

1. Define dichotomous and manifold classification.
2. For two attributes A and B if (AB)=20, (Aβ)=25 ,(αB)=32 and N=100 ,find

(A) and (B)

1. Write the conditions for the consistency of data for three attributes.
2. State the axiomatic definition of probability.
3. When do you say that three events A,B and C are independent?
4. Define binomial distribution.
5. What are TypeI and TypeII errors in testing of hypothesis.
6. Write any two applications of chi-square distribution.
7. Write a note on chance and assignable causes in quality control.
8. State the control limits for p chart.

PART-B

Answer any five questions.                                                                           5×8=40 marks

1. Can vaccination be regarded as a preventive measure for small-pox from the

data given below?

“Of 1482 persons in a locality exposed to small-pox ,368 in all were attacked.”

“Of 1482 persons ,343 had been  vaccinated and of these only 35 were attacked.”

1. For n attributes A1,A2,…An, show that

(A1 A2,…An)(A1) + (A2) +…. +(An)-(n-1)N, where N is the total number of

observations.

1. If 10 fair coins were tossed simultaneously, find the probability of getting

1. 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

then show that (X-)/ follows standard normal distribution.

(b) Write any four characteristics of normal distribution.

1. 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.

1. 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 .

PART-C

Answer  any two questions.                                                                      2×20 = 40 marks

1. (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)|X-30| >5.

1. 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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