B.Sc Economics Question Paper

Loyola College B.Sc. Economics April 2010 Advanced Statistical Methods Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc., B.Com., DEGREE EXAMINATION – ECONOMICS & COMMERCE

THIRD SEMESTER – APRIL 2011

ST 3202/3200/4205/4200 – ADVANCED STATISTICAL METHODS

 

 

Date : 15-04-2011              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION A                                           (10 X 2 = 20 marks)

     Answer ALL questions.         

                                  

  1. What is meant by independence of attributes?
  2. What are the types of sampling?
  3. Define Probability of an event.
  4. Define conditional probability.
  5. State any two properties of normal distribution.
  6. State Central Limit Theorem.
  7. State Type – I and Type – II error.
  8. What is meant by analysis of variance?
  9. Explain the various types of control chart.
  10. What is meant by probable error? Mention its uses.

 

SECTION B                                              (5 X 8 = 40 Marks)

     Answer any FIVE questions

 

  1. State and prove multiplication theorem.

 

  1. 800 candidates of both sex appeared at an examination. The boys outnumbered the girls by 15 %

of  the total. The number of candidates who passed exceeded  the number failed by 480. Equal

number of boys and girls failed  in the examination. Prepare a 2×2 table and find the coefficient

of association and Comment.

 

  1. Five men in a company of 20 are graduates, if 3 men are picked out from this 20 at random, what is the probability that (i) all are graduate (ii) at least one is a graduate.

 

  1. Two random samples of sizes 400 and 500 have mean 10.9 and 11.5 respectively. Can the samples be

regarded as drawn from the same population with variance 25?  Test at 1% level.

  1. The following data is collected on two characteristics:
  Smokers Non-Smokers
Literate 83 57
Illiterate 45 68

Based on this test whether there is relation between the habit of smoking and literacy.

 

16 . A company arranged an intensive training course for its team of salesmen. A random sample of 10       salesmen was selected and the value ( in 000) of their sales made in the weeks immediately before and     after the course are shown in the following table:

Salesman 1 2 3 4 5 6 7 8 9 10
Sales before Training 12 23 5 18 10 21 19 15 8 14
Sales after Training 18 22 15 21 13 22 17 19 12 16

 

 

 

 

 

 

Test whether there is evidence of an increase in mean sales. Test at 5% level

 

  1. State the advantages and disadvantages of statistical quality control.

 

 

 

 

  1. The number of defects detected in 20 items are given below

Item No       :  1   2    3    4     5    6   7    8     9    10    11     12    13    14   15   16   17   18  19    20

No. of defects         :  2    0   4   1      0     0   8     1    2     0      6        0     2      1    0      3    2      1   0    2

Test whether the process is under control. Device a suitable scheme for future

 

 

SECTION   C                                   (2 X 20  =  40 Marks)

Answer any TWO questions

 

19.(a) A number of school-children were examined for the presence or absence of certain

defects of which three chief descriptions were noted; A-development defects;

B-nerve signs; C low nutrition. Given the following ultimate frequencies, find the

frequencies of the classes defined by the presence of the defects.

(ABC) = 57; (aBC) = 78

(ABg) = 281; (aBg) = 670

(AbC) = 86; (abC) = 65

(Abg) = 453; (abg) = 8310                                                                                            (10)

19 . (b)  A factory manufacturing television has four units A, B, C and D. The units A, B, C and D manufacture 15%, 20%, 30%, and  35%, of the total output respectively. It was found that out of their outputs 1%, 2%, 2% and 3% are defective. A television is chosen at random from the output and found to be defective. What is the probability that, it came from unit D?                                                            (10)

 

  1. (a) If 10% of the screws produced by an automatic machines are defectives, find the probability

that out of 20 screws selected at random there are (i) exactly two defectives

(ii)at the most three defectives  (iii) at least two defectives                                               (10)

 

  1. (b) The average daily sales of 500 branch offices was Rs.150,000 and the standard deviation

Rs.15,000. Assuming the distribution to be normal, find how many branches have sales between

  • 1,20,000 and Rs.1,45,000
  • 1,40,000 and Rs.1,60,000                                                (10)

21.(a)Random samples of 400 men and 600 women were asked whether they would like to have a fly-over near their residence 200 men and 325 women were in favor of it. Test the equality of proportion of men and  women in the proposal? Test at 5% level.                                                                 (10)

 

  1. (b) Value of a Variety in two samples are given below:
Sample I 5 6 8 1 12 4 3 9 6 10
Sample II 2 3 6 8 1 10 2 8 * *

 

 

 

 

Test the significance of the difference between the two sample means.                                            (10)

 

  1. Develop the Two- way ANOVA for the following data:

 

                                                                  Treatment

 

A B C D
I 3 4 6 6
II 6 4 5 3
II 6 6 4 7

 

 

Plots of land

 

 

 

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Loyola College B.Sc. Economics April 2012 Econometrics Question Paper PDF Download

by

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – ECONOMICS

FOURTH SEMESTER – APRIL 2012

ST 4207 – ECONOMETRICS

 

 

Date : 19-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

Section –A                                         

Answer all the questions                                                                                           (10 x 2 = 20)

  1. Define Maximum likelihood estimation.
  1. Give any two properties of normal distribution.
  2. Mention the difference between statistic and parameter.
  1. What is level of significance?
  2. Distinguish between R2 and adjusted R2
  3. What is meant by Intercept and Slope?
  4. Define Multicollinearity.
  5. Give any two forms of Glesjer test.
  6. State the reason for lag.
  7. Define specification error.

 

Section –B                                               

         

 Answer any five questions                                                                                         (5 x 8 = 40)

  1. Data on the readership of a certain magazine show that the proportion of male readers under 35 is 0.40 and over 35 is 0.20. If the proportion of readers under 35 is 0.70, find the proportion of subscribers that are female over 35 years. Also calculate the probability that randomly selected male subscriber is under 35 years of age.

 

  1. A random variable X has the following probability distribution function:

 

Value of X, x 0 1 2 3 4 5 6 7 8
P(x) K 3k 5k 7k 9k 11k 13k 15k 17k

 

  1. Determine the value of k
  2. Find P( X < 3) , P( X 3)
  • P ( 0 < X < 5 )

 

  1. Establish the unbiasedness property of OLS estimators for simple linear regression model.
  2. State and prove Gauss Markov theorem.
  3. Derive  by using matrix approach for a multiple regression model.
  4. How do you measure the goodness of fit in the regression model.

 

 

  1. Consider the model with the following observations on Y and X
X 1 2 3 4 5 6 7 8 9 10
Y 2 2 3 3 3 1 4 5 5 2

The estimated model is =1.933+0.194X; Examine the existence of heteroscedasticity

using spearman’s rank correlation test.

  1. Explain lagged variable with an illustration.

 

 

Section – C                                              

         

 Answer any two questions                                                                                         (2 x 20= 40)

  1. a) A variable X is distributed between the values 0 and 4 and its probability density function is given by

Find the value of k, the mean and standard deviation of the distribution.

  1. b) Write short notes on:-
  2. Nature of Econometrics
  3. Structural and reduced forms
  • Applications  of Econometrics

 

  1. Given the following data

 

∑ Yi2 1000
∑ X1i2 200
∑X2i2 100
∑ X1i  Yi 400
∑ X2i  Yi   -100
∑ X1i  X2i 0
50
15
10
n 28

 

  1. Estimate the parameter in the equation,
  2. Estimate S.E. of estimators,
  3. Test the significance of   and
  4. Find R

 

  1. Given the following data test the problem of heteroscedasticity with the help of Goldfeld Quantt

 

X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Y 2 2 2 1 3 5 8 11 12 10 10 12 15 10 11

 

 

  1. Consider the following data on Y, X1 and X2.

Y:        10        20        40        30        50

X1:       2          5          3          8          7

X2:       1          0          1          2          1

a.) Fit a linear model of Y on X1 and X2. Interpret the regression coefficients.

b.) Calculate R2 and interpret it.

 

 

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Loyola College B.Sc. Economics April 2012 Advanced Statistical Methods Question Paper PDF Download

by

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A., B.COM., DEGREE EXAMINATION – ECONOMICS & COMMERCE

THIRD SEMESTER – APRIL 2012

ST 3202/3200/4205/4200 – ADVANCED STATISTICAL METHODS

 

 

Date : 02-05-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION A

     Answer ALL questions.                                                                                           (10 X 2 = 20 marks)    

                                  

  1. State the axioms of the Probability .

 

  1. Write any four properties of normal distribution.
  2. Define conditional probability.
  3. State Type – I and Type – II error.

 

  1. What is standard normal Variable?
  2. State Central Limit Theorem.

7.What is null hypothesis?

  1. What is meant by independence of attributes?
  2. Distinguish between np chart and p chart.
  3. Distinguish between the control limits and tolerance limits.

 

SECTION B

     Answer any FIVE questions:                                                                              (5 X 8 = 40 Marks)

 

  1. 800 candidates of both sex appeared in an examination. The boys outnumbered the girls by 15 %

of  the total. The number of candidates who passed exceeded  the number failed by 480. Equal

number of boys and girls failed  in the examination. Prepare a 2×2 table and find the coefficient

of association and Comment.

 

  1. State and prove Baye’s theorem.
  2. A Sub-Committee of 6 members is to be formed out of a group consisting of 7

men and 4 women. Calculate the probability that the sub-committee will consist of

(1) exactly 2 women (2) at least 2 women.

  1. Two random samples of sizes 400 and 500 have mean 10.9 and 11.5 respectively. Can the samples be

regarded as drawn from the same population with variance 25?  Test at 1% level.

  1. What is Sampling Technique ? Explain different types of Sampling.

 

  1. In a survey of 200 boys, of which 75 intelligent, 40 had skilled fathers while 85 of the Unintelligent  boys has unskilled fathers. Do these figures support the hypothesis that skilled fathers have intelligent boys. Use Chi square –test of 5 % level.

 

 

  1. State the advantages and disadvantages of statistical quality control.

 

  1. The number of defects detected in 20 items are given below

Item No       :  1   2    3    4     5    6   7    8     9    10    11     12    13    14   15   16   17   18  19    20

No. of defects      :  2    0   4   1      0     0   8     1    2     0      6        0     2      1    0      3    2      1   0      2

Test whether the process is under control. Device a suitable scheme for future

 

SECTION   C                                  

Answer any TWO questions:                                                                                   (2 X 20  =  40 Marks)

19.(a) Given (ABC) = 137;   (αBC) = 261; (ABC) = 313; (Aβg) = 284; (Abr) = 417; (αBg) = 420;

(αbC)  =  490; (abg)  =  508; Find the frequencies (AB), (A) and N.                       (10)

 

19.(b) Two Urns contain respectively 10 white, 6 red and 9 black and 3 white 7 red and 15 black balls.  One ball is drawn from each Urn.  Find the probability that  (i)  Both balls are red   (ii)  Both balls are of the same colour.                                                                                                                             (10)

 

  1. (a) A Company has four production sections viz. S1, S2, S3 and S4 , which contribute 30%, 20%, 28%    and  22% of the total output. It was observed that those sections  respectively produced 1%, 2%, 3% and 4% defective units. If a unit is selected at  random and found to be defective, what is the probability that   the units so selected has  come from either S1 or S4.?                                         (10)

 

  1. (b) The customer accounts of a certain departmental store have an average balance of Rs.120 and a

standard deviation of Rs.40. Assuming that the account balances are normally distributed, find

  • What proportion of accounts is over Rs.150?
  • What proportion of accounts is between Rs.100 and Rs.150?
  • What proportion of accounts is between Rs.60 and Rs.90?                (10)

 

21.(a) A random samples of 400 men and 600 women were asked whether they would like to have a fly-over near their residence. 200 men and 325 women were in favor of it. Test the equality of proportion of men and women at 5% level.                                                                                  (10)

  1. (b) Value of a Variety in two samples are given below:
Sample I 5 6 8 1 12 4 3 9 6 10
Sample II 2 3 6 8 1 10 2 8 * *

 

 

 

Test the significance of the difference between the two sample means.                                            (10)

 

  1. Prepare a Two- way ANOVA on the data given below.

 

                                                         Treatment I

 

I II III
A 30 26 38
B 24 29 28
C 33 24 35
D 36 31 30
E 27 35 33

 

 

 

Treatment I I 

 

 

 

Use the coding method, subtracting 30 from the given numbers.                                                                                                                                                                                                                              (20)

 

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