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  ANDHRA LOYOLA COLLEGE, (AUTONOMOUS), VIJAYAWADA – 520 008.

II-B.A./B.Sc.                        STATISTICS                               Paper-III

STATISTICAL METHODS & ESTIMATION   Re-Mid Sep2014

TIME: 2 Hrs                                                                     Max Marks: 100

PART-A

Answer ALL Questions:                                                                    8X10=80

1. a) Define Karl Pearson’s correlation coefficient and state any two

    Properties of correlation coefficient.

OR

b) Prove that

2. a) Obtain Karl Pearson’s correlation coefficient to the following data:

X	65	66	67	67	68	69	70	72
Y	67	68	65	68	72	72	69	71

                                                          OR

b) Calculate spearman’s rank correlation coefficient for the following data.

X	23	33	41	50	43	38	49	38
Y	42	46	47	36	35	36	14	36

SECTION – II

3. a) Derive the Regression line of Y on X.

OR

b) In a tri-variate distribution  find  

.

                                                SECTION-III

4.  a) Show that for n attributes

where N is the total no of observations.

                                                OR

b) Among the population of a certain town 50% of males 60% are of wage earners and 50% are 45 years of age or over, 10% of males are not wage earners and 40% are under 45. Make the best possible inference about the limits within which the percentage of persons(males or females) 45 years or over are wage earners.

     5.  a) Explain the conditions for consistency of three attributes.

OR

          b) Define Yule’s coefficient of Association and Show that

SECTION -IV

     6. a)  Explain (i) Population     (ii) Sample             (iii) Statistic

     (iv) Parameter    (v) Sampling Distribution

                                      OR

b)   Define -distribution and also state its properties and applications.

SECTION -V

7. a) Explain the criteria of a good estimator and Show that if t is a consistent estimator of the population parameter then t² is a consistent estimator of the population parameter ².

                                                OR

b) Find the MLE of the parameter  of Poisson distribution and also obtain its variance.

8. a) State and Prove Cramer Rao inequality.

OR

b) Obtain the 95% and 99% confidence interval for population mean in

case of a normal population.

Part-B

9. Choose the correct answer and write it in the answer book.        1x10=10

a) In case of three attributes, the total number of class frequencies is ______

          3²                 2³                 3³                 2²

b) Correlation coefficient is the _______ of the regression coefficients

A.M              G.M              H.M              None

c) When there is a perfect +ve association between two attributes Q would  

    be

          0                 -0.9             -1                +1

d)  if r_xy=0 then the lines of regression are

          parallel         perpendicular                   coincide        none

e) An estimator t of a parameter  is said to be unbiased if ___

E(t)=                   E(t)>                   E(t)<          None

f) Fishers-Neymann factorization theorem is due to

Sufficiency    Unbiasedness         Consistency            None

g) The term regression was first used by

Galton                   Newton        Tanns           None

h) Square of a standard normal variate is known as

F-statistic     -variate    t-statistic      None

i) x+2y-5=0, 2x+3y=8 are the regression lines then the mean values are

(2,1)            (1,2)            (2,5)            (2,3)

j) Mean of distribution is

          n        2n      3n      4n

10. Fill in the blanks with suitable answer.                                    1x10=10

a.    If A  & B are positively associated, then a & b are  _____________ associated.

b.    For testing the goodness of fit we use ____________ distribution.

c.    S.E. (p) = _______________.

d.    Yule’s coefficient of association lies between ____ and ____.

e.    If t ~ t _n then t² ~ ___________________.

f.     In a dichotomous classification with n attributes, the number of class frequencies of order r is ___________________.

g.    b₁ of chi-square distribution is ___________.

h.  Limits for Spearman’s rank correlation coefficient are __________.

i.   Regression coefficients are independent of _________.

10. If E() =  then  is called _______________ of .

ANDHRA LOYOLA COLLEGE, (AUTONOMOUS)::VIJAYAWADA – 520 008.

II-B.Sc./B.A.          KEY TO MODEL QUESTION PAPER         III END SEMESTER

                          STATISTICAL METHODS & ESTIMATION

TIME: 3 Hrs                                   STATISTICS                     Max Marks: 100

Scheme of valuation

PART-A

SECTION-I

1. a) Karl Pearson’s correlation coefficient                                        -2Marks

        Derivation of two  properties                                           2x4=8Marks

                                                          OR

    b) Derivation                                                                           -10Marks

2. a) Problem Solving                 Ans: r = 0.6                                 -10Marks

                                                          OR

    b) Problem Solving                 Ans:  = - 0.43                          -10Marks

SECTION-II

3. a) Derivation of regression line of Y on X                                   -10Marks

                                                         OR

    b) Problem Solving       Ans: =0.2425       =0.7211     

                                                b_12.3=0.4           b_13.2=0.1333       -10Marks

                                                SECTION-III

4.    a) Theorem proof                                                                  -10 Marks

                                                     OR

b) Problem solving:    Best possible limits are 25 and 45            -10 Marks

5. a) Conditions for consistency                                                   -10 Marks

                                                          OR

b) Yule’s coefficient of Association                                             -2 Marks

    proof of                                                               -8 Marks

                                                SECTION-IV

6.    a) Population                                                                          -2Marks

         Sample                                                                               -2Marks

         Parameter                                                                           -2Marks

         Statistic                                                                              -2Marks

Standard error                                                                    -2Marks

                                                          OR

    b) Definition of chi-square distribution                                        -3Marks

        Properties                                                                            -4Marks

       Applications                                                                          -3Marks

SECTION-V

7. a) Unbiased ness                                                                      -1½ Marks

       Consistency                                                                          -1 ½ Marks

       Sufficiency                                                                            -1 ½ Marks

  Efficiency                                                                             -1 ½ Marks

  Problem Solving                                                                    -4Marks

                                                          OR

    b)   Problem solving:  and variance of MLE =                  -10Marks

8. a) Theorem Proof                                                                                -10Marks

                                                          OR

    b) 95% confidence limits:                                       -5 Marks

          99% confidence limits:                                     -5 Marks

PART-B

9. FILL IN THE BLANKS:

1. 3³
2. G.M
3. +1                                 
4. perpendicular
5. E(t)=
6. Sufficiency
7. Galton
8. -variate
9. (1,2)                    
10. n     

                             .

10. CHOOSE THE CORRECT ANSWER

      a)      Positively associated

      b)      Chi-square distribution

      c)             

     d)      -1 and +1

      e)     

       f)     

      g)      8/n

      h)     

        i)      Change of origin

        j)      Unbiased estimator

ANDHRA LOYOLA COLLEGE, (AUTONOMOUS) VIJAYAWADA – 520 008.

II-B.A./B.Sc.                                      STATISTICS                                                       Paper-IV

IV END SEMESTER MODEL QUESTION PAPER

TIME: 3 Hrs                   TESTING OF HYPOTHESIS                                     Max Marks: 100

PART-A

Answer ALL Questions:                                                                                             8X10=80

                                                                        Unit-I

1. a) State and Prove Neymann Pearson Lemma.

Or

            b) Let ‘p’ be probability that a coin will fall head in a single toss in order to test

               H₀:p=1/2 Vs H₁:p=3/4. The coin is tossed 5 times and H₀ is rejected if more

               than 3 heads are obtained. Find the probability of Type I error and Power of

               the test.

                                                            Unit-II

2. a) Two independent samples of sizes 5 and 6 had the following values.

Sample I:   9, 10, 13, 12, 6

Sample II: 10, 9, 11, 14, 6, 10

            Is there any significant difference between the two population

    variances?

                                                            Or

b) Explain the test procedure of t-test for difference of means.

3. a) Explain the procedure of t-test for single correlation co-efficient.

                                                                Or

             b) A company is engaged in the manufacture of car tyres. Their mean life is 42,000 km

with a standard deviation of 3,000 km. a change in the production process is believed to improve the quality of tyres. A test sample of 28 new tyres has a mean life of 43,500 km. do you think that the new car tyres are significantly superior to the earlier one? Test the hypothesis at 5 % level of significance.

Unit-III

4. a) In a year, there are 956 births in a town A of which 52.5% were males, while

    in a town A and town B combined this proportion in a total of 1406 births

    were 0.496. Is there any significant difference in the proportion of male births

    in the two towns?

                                                            Or

b) Explain the test procedure for difference of Standard deviations.

5. a) In a sample of 1000 people in Maharastra 540 are rice eaters and rest are

    wheat eaters. Can we assume that both rice and wheat eaters are equally

    popular in this state at 1-% level of significance?

Or

b)  Explain the test procedure for single mean and single proportion.

                                                                  Unit-IV

6. a) What are the advantages and disadvantages of non-parametric tests.

Or

b) The following arrangement shows the rise (U) or fall (D) in the price of an equity

                  share on 40 consecutive trading days on which its price did not remain the same:

                        UUDDUUUDUUUDDUDDDUDDUDDUUUUDDDUUDDUUDDDU

                  Test the hypothesis that this arrangement of U’s and D’s is random at 5% los.

7. a) Explain the procedure for Median test.

                                                                           Or

b) Apply sign test to examine whether the following samples are drawn from populations

   with same probability density function or not.

                        Sample I:         10        13        16        21        18        17       

            Sample II:       14        12        19        23        18        14

     

                                                            Unit-V

8.    a) Explain the test procedure of chi-square test for independence of

   attributes.

                                                            Or

             b) Explain the procedure of S.P.R.T.

Part-B

9. Choose the correct answer and write it in the answer book.          1x10=10

a)      out of the two types of errors the more severe error is

type I error                                                      type II error                            

both type/ I & II error                         No error is severe

b)      To test an hypothesis about proportions of items in a class the usual test is

t-test                F-test               Z-test               -test

c)      The degrees of freedom for t-statistic in paired t-test based on n pairs of observations is

2(n-1) n-1                   2n-1                 None of these

d)     For large samples the sample size should be

>25                  >35                  >30                 

e)      Standard error of proportion p

                                              

f)       _______ is used to test the homogeneity of independent estimates of

  the population variance.

      F-test               t-test                -test            None

g)      ________ test does not make any assumption regarding the form of

the population.

Non-parametric test                sign test           signed rank test           -test

h)      _________ test is used for test for randomness.

            Run test                       sign test                       signed rank test              U-test

i)        _______ test is a statistical procedure for testing if two independent ordered samples differ in their central tendencies.

Sign test                      Median                        Run                 None

j)        For testing the hypothesis that =10, given that s=15 for n=20, which test if preferable

t-test                F-test               Z-test               -test

10. Fill in the blanks with suitable answer.                                         1x10=10

a)    _____________ provides most powerful test of simple hypothesis against a simple alternative hypothesis.

b)   ___________ found applications in psychometry.

c)    Paired t-test is applicable in case of ___________ samples only. 

d)   The size of a test is equal to the area of the __________________.

e)    A randomized test does not involve any____________.

f)     In working with a contingency table of order 4x5 the d.f for chi-square is _____.

g)   In case of large samples, Mann-Whitney U is distributed with mean ___________ and variance ____________.

h)   In quality control terminology Type I error is ______________ risk.

i)     Non parametric statistical methods are applicable even if the measurements are on _______________ scale.

j)     Critical region is also known as ___________.

ANDHRA LOYOLA COLLEGE, (AUTONOMOUS)::VIJAYAWADA – 520 008.

KEY TO MODEL QUESTION PAPER

II-B.A./B.Sc.                       IV END SEMESTER                                    Paper-III

TESTING OF HYPOTHESIS

TIME: 3 Hrs                                       STATISTICS                                                      Max Marks: 100

Scheme of valuation

PART-A

UNIT-I

1. a) N-P Lemma proof                                                                                              -10 Marks

                                                                        Or

   b) Problem Solving  Ans:                                -10 Marks

                                                                        Unit-II

2. a) Problem Solving Ans: F=1.1029, Accept H₀                                             -10Marks

                                                                        Or       

    b) Explaining the Procedure                                                                                     -10Marks

3. a)  Explaining the Procedure                                                                                      -10Marks     

                                                                      Or

    b) Problem Solving             Ans: t=2.645, Reject H₀                                                -10Marks                               

                                                                        Unit-III

4. a) Problem Solving Ans: Z= 3.4356, Reject H₀                                           -10Marks

                                                                        Or

   b) Explaining the Procedure                                                                                      -10Marks

5. a) Problem Solving Ans: Z= 2.5316, Reject H₀                                           -10Marks

                                                                        Or

    b) Explaining the Procedure                                                                                     -10Marks

                                                                        Unit-IV

6. a) Advantages and Disadvantages of Non parametric tests                                     -10Marks

                                                                        Or

    b) Problem Solving                         Ans: Z= -0.645, Accept H₀                               -10Marks

7. a) Explaining the Procedure                                                                                      -10Marks

                                                                        Or

   b) Problem Solving                              Ans: p’= 0.5 Accept H₀                                              -10Marks

                                                                                Unit-V

8. a) Explaining the Procedure                                                                                      -10Marks

                                                                        Or

    b) Procedure of S.P.R.T                                                                                                            -10Marks

PART-B

8. FILL IN THE BLANKS:

1. Type II error
2. Z-test
3. n-1
4. >30
5. 
6. F-test
7. Non-parametric test
8. Run test                                  .
9. Median test
10. - test

                

                                 .

9.      CHOOSE THE CORRECT ANSWER

1. N P Lemma
2. Non-parametric test
3. Paired samples
4. Critical region
5. test statistic
6. 12
7.  and
8. consumers risk
9. nominal     
10. Rejection region

ANDHRA LOYOLA COLLEGE (AUTONOMOUS): VIJAYAWADA – 8.

III-B.A./B.Sc.                                  PAPER – V                                   SEPTEMBER -2013       II-MID                                     STATISTICS                               MODEL PAPER SAMPLE SURVEYS AND DESIGN OF EXPERIMENTS

Duration: 2Hrs                                                                                         Max Marks: 100

PART-A

                                                                                                                                   

                                                                                                                 

Answer  All  The  Five  Questions , Each question carry equal marks :             

                                                                                                                  5 X 18 = 90 Marks

1. A.   Explain the advantages of sampling over complete census , also give the limitations of sampling.

                                                 (OR)

B.  Define sample and population. What are the principle steps in conducting  sample surveys

    2.      A.  Show that SRSWOR, the sample mean square is an unbiased estimate of     population mean square .      

                                                                     (OR)

              B. In SRSWOR give the equation for variance and solve that equation upto finite population correction.

 3.   A.  Give the equation for variance in Stratified random sampling with respect to optimum allocation for fixed sample size ‘n’ .                        

                                                       (OR)

      B.   Show that Variance of Optimum allocation  ≤ Variance of Proportional allocation ≤ Variance of Simple random sample with out replacement (srswor) .

4.  A Give the complete analysis of ANOVA two -way classification.

                                           (OR)

       B. .   Define latin square and latin square design and explain the analysis of L.S.D

5.  A. Discuss the analysis of 2² factorial design

                                                  (OR)

      B. Explain the functions and organization of NSSO

 ,                                                           PART-B

Fill  in the  blanks :                                                                                   10 X 1 = 10 Marks

1.The term ANOVA was introduced by........................................

2. Heterogeneous experimental material can be made homogeneous by ............

3. In ANOVA two-way classification, the total no.of observations, N = ......................

4. Sampling error can be decreased by increasing ...........................

5. No.of possible samples of size ‘n’ that can be drawn from a finite population of size ‘N’   is.......................................

6.Dividing the whole experimental area into homogeneous classes the chance error exists in........

7. Raw sum of squares can be obtained by.....................                 

8.  Missing value can be estimated in L.S.D.  by................................

9.  In 2³  factorial design we have .....................

10. The no.of draws are dependent in..........................sampling.