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
- a) Define Karl Pearson’s
correlation coefficient and state any two
Properties of correlation coefficient.
OR
b) Prove
that 
- 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
- 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
- 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.
- 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 rxy=0 then the lines of
regression are
parallel perpendicular coincide none
e)
An estimator t of a parameter 
is said to be unbiased
if ___
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
_________.
- 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
b12.3=0.4
b13.2=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:
- 33
- G.M
- +1
- perpendicular
- E(t)=
- Sufficiency
- Galton
- -variate
- (1,2)
- 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
- 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
- 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.
- 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
- 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.
- 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
- 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.
- 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
- FILL IN THE BLANKS:
- Type II error
- Z-test
- n-1
- >30
- F-test
- Non-parametric test
- Run test .
- Median test
- - test
.
9.
CHOOSE THE CORRECT ANSWER
- N P Lemma
- Non-parametric test
- Paired samples
- Critical region
- test statistic
- 12
- and
- consumers risk
- nominal
- 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.
