University Of Pune Question Paper
T.Y. B.A. Examination, 2010
APPLIED STATISTICS (General)
Applications of Statistics
Time: 3 Hours Max. Marks: 80
N.B. : i) All questions are compulsory.
ii) Figures to the right indicate full marks.
iii) Use of calculator and statistical table is allowed.
iv) Notations and abbreviations have their usual meanings.
1. Attempt any ten of the following : [2 each]
a) Define cumulative distribution function of a continuous random variable (r.v.).
b) State any two properties normal distribution.
c) Let X → N (4, 16). Find [ ] ≥ 4.6XP .
d) Explain the term ‘Alternative hypothesis’ with illustration.
e) State the formula of STDR in case of direct method.
f) Define Net Reproduction Rate (NRR).
g) Explain the term process control.
h) State any two measures of fertility rate and any two measures of mortality rate.
i) State the test statistic for testing H0 : μ = μ0 against 1 0 :H μ > μ , when large
sample is drawn from the population.
j) Write and explain the terms used in mathematical model used for one way
analysis of variance.
k) Explain in brief concept of distribution free statistic.
l) Explain the term ‘chance causes’ of quality variations.
m) State the interpretation of low spots on p-chart.
2. Attempt any two of the following : [5 each]
a) If X is a r.v. with probability density function (p.d.f.)
= x/k)x(f ; 0 < x < 4
= 0 ; otherwise
Find the value of constant k and obtain distribution function of X.
b) For a certain normal distribution, exactly 8% of the items are below 40 and
90% items are below 60. Find the mean and standard deviation of the
distribution.
c) Explain the test procedure for testing H0 : P = P0 against
H1 : P < P0, where P is population proportion.
d) Describe the procedure of construction of C chart when standards are not
given. P.T.O.
3. Attempt any two of the following : [10 each]
a) i) A nitrogen fertilizer was used on 10 plots and mean yield per plot was
found to be 82.5 bushels with standard deviation equal to 10 bushels. On
the other hand, 15 plots treated with phosphate fertilizer gave a mean yield
of 90.5 bushels per plot with standard deviation equal to 20 bushels. Test
at 5% level of significance whether the two fertilizers are significantly different
on the basis of the mean yield. 6
ii) Describe the procedure to test 2
2
2
10 :H σ=σ against 2
2
2
11 :H σ>σ . 4
b) i) Compute STDR for the local population from the following data
Age Group
Local Population Standard
Population ASDR Population
0-5 30000 100 50000
5-15 35000 25 60000
15-40 65000 10 160000
40 and above 20000 30 30000
6
ii) Explain in brief distinction between a parametric and non-parametric
problems. 4
c) Given below are the values of sample mean X and the range (R) for ten
samples of size 5 each :
Sample Number Range Mean
1 4 35
2 5 34
3 4 30
4 6 36
5 637
6 331
7 735
8 532
9 336
10 5 34
Set up X and R-charts, examine the state of control of the given process.
Comment on your results. 10
-3- [3801] – 378
d) i) The following data on vaccination was collected in a hospital to find out
whether vaccination reduces the severity of any attack of swine flu.
Severe Not severe
Vaccinated 50 750
Not vaccinated 80 10
Test whether the vaccination and severity are associated. Use 5% level of
significance. 5
ii) Explain concept of analysis of variance. 5
4. Attempt any two of the following : [15 each]
a) i) Describe large sample test for testing H0
: μ1 = μ 2
against H1 : μ 1
≠ μ 2
. 5
ii) Complete the following analysis of variance table : 5
Source of
variation
Degrees of
freedom
Sum of
squares
Mean sum of
squares
F-ratio
Treatment ? 220 ? ?
Error 15 ? ?
Total 19 560.2
iii) Define the following terms :
Crude Death Rate (CDR),
Age Specific Fertility Rate (ASFR),
Gross Reproduction Rate (GRR). 5
b) i) Let X and Y be two independent normal variables with means 4, 6 and
variances 16, 25 respectively. Find
I) P (6X + Y > 10)
II) P ( | X – Y | < 2) 5
ii) Test the randomness of the sequence of defective (D) and non-defective
items (N) in the sample given below :
NNDDDDNDNDDDN
Use 5% level of significance. 5
iii) Define the following terms :
Critical region, level of significance, statistic. 5
c) i) Compute Gross Reproduction Rate (GRR) and Net Reproduction Rate
(NRR) for the following data : 10
Age-Group Female Population
(in '000)
No. of female
births
Survival
rate
15-19 140 4500 0.92
20-24 110 11700 0.89
25-29 102 9200 0.88
30-34 96 3900 0.87
35-39 102 1050 0.85
40-44 97 480 0.84
45-49 91 140 0.82
ii) Describe the sign test. 5
d) i) The following table is obtained from the inspection on completed units of
a product in 20 lots of size 100 each.
Lot No. 1 2 3 4 5 6 7 8 9 10
No. of Defectives 4 9 11 7 5 4 5 2 2 4
Lot No. 11 12 13 14 15 16 17 18 19 20
No. of Defectives 3672243957
Set up an appropriate control chart and comment on the state of control. 10
ii) Describe the procedure of the Chi-square test of goodness of fit. 5
_________________
T.Y. B.A. Examination, 2010
APPLIED STATISTICS (General)
Applications of Statistics
Time: 3 Hours Max. Marks: 80
N.B. : i) All questions are compulsory.
ii) Figures to the right indicate full marks.
iii) Use of calculator and statistical table is allowed.
iv) Notations and abbreviations have their usual meanings.
1. Attempt any ten of the following : [2 each]
a) Define cumulative distribution function of a continuous random variable (r.v.).
b) State any two properties normal distribution.
c) Let X → N (4, 16). Find [ ] ≥ 4.6XP .
d) Explain the term ‘Alternative hypothesis’ with illustration.
e) State the formula of STDR in case of direct method.
f) Define Net Reproduction Rate (NRR).
g) Explain the term process control.
h) State any two measures of fertility rate and any two measures of mortality rate.
i) State the test statistic for testing H0 : μ = μ0 against 1 0 :H μ > μ , when large
sample is drawn from the population.
j) Write and explain the terms used in mathematical model used for one way
analysis of variance.
k) Explain in brief concept of distribution free statistic.
l) Explain the term ‘chance causes’ of quality variations.
m) State the interpretation of low spots on p-chart.
2. Attempt any two of the following : [5 each]
a) If X is a r.v. with probability density function (p.d.f.)
= x/k)x(f ; 0 < x < 4
= 0 ; otherwise
Find the value of constant k and obtain distribution function of X.
b) For a certain normal distribution, exactly 8% of the items are below 40 and
90% items are below 60. Find the mean and standard deviation of the
distribution.
c) Explain the test procedure for testing H0 : P = P0 against
H1 : P < P0, where P is population proportion.
d) Describe the procedure of construction of C chart when standards are not
given. P.T.O.
3. Attempt any two of the following : [10 each]
a) i) A nitrogen fertilizer was used on 10 plots and mean yield per plot was
found to be 82.5 bushels with standard deviation equal to 10 bushels. On
the other hand, 15 plots treated with phosphate fertilizer gave a mean yield
of 90.5 bushels per plot with standard deviation equal to 20 bushels. Test
at 5% level of significance whether the two fertilizers are significantly different
on the basis of the mean yield. 6
ii) Describe the procedure to test 2
2
2
10 :H σ=σ against 2
2
2
11 :H σ>σ . 4
b) i) Compute STDR for the local population from the following data
Age Group
Local Population Standard
Population ASDR Population
0-5 30000 100 50000
5-15 35000 25 60000
15-40 65000 10 160000
40 and above 20000 30 30000
6
ii) Explain in brief distinction between a parametric and non-parametric
problems. 4
c) Given below are the values of sample mean X and the range (R) for ten
samples of size 5 each :
Sample Number Range Mean
1 4 35
2 5 34
3 4 30
4 6 36
5 637
6 331
7 735
8 532
9 336
10 5 34
Set up X and R-charts, examine the state of control of the given process.
Comment on your results. 10
-3- [3801] – 378
d) i) The following data on vaccination was collected in a hospital to find out
whether vaccination reduces the severity of any attack of swine flu.
Severe Not severe
Vaccinated 50 750
Not vaccinated 80 10
Test whether the vaccination and severity are associated. Use 5% level of
significance. 5
ii) Explain concept of analysis of variance. 5
4. Attempt any two of the following : [15 each]
a) i) Describe large sample test for testing H0
: μ1 = μ 2
against H1 : μ 1
≠ μ 2
. 5
ii) Complete the following analysis of variance table : 5
Source of
variation
Degrees of
freedom
Sum of
squares
Mean sum of
squares
F-ratio
Treatment ? 220 ? ?
Error 15 ? ?
Total 19 560.2
iii) Define the following terms :
Crude Death Rate (CDR),
Age Specific Fertility Rate (ASFR),
Gross Reproduction Rate (GRR). 5
b) i) Let X and Y be two independent normal variables with means 4, 6 and
variances 16, 25 respectively. Find
I) P (6X + Y > 10)
II) P ( | X – Y | < 2) 5
ii) Test the randomness of the sequence of defective (D) and non-defective
items (N) in the sample given below :
NNDDDDNDNDDDN
Use 5% level of significance. 5
iii) Define the following terms :
Critical region, level of significance, statistic. 5
c) i) Compute Gross Reproduction Rate (GRR) and Net Reproduction Rate
(NRR) for the following data : 10
Age-Group Female Population
(in '000)
No. of female
births
Survival
rate
15-19 140 4500 0.92
20-24 110 11700 0.89
25-29 102 9200 0.88
30-34 96 3900 0.87
35-39 102 1050 0.85
40-44 97 480 0.84
45-49 91 140 0.82
ii) Describe the sign test. 5
d) i) The following table is obtained from the inspection on completed units of
a product in 20 lots of size 100 each.
Lot No. 1 2 3 4 5 6 7 8 9 10
No. of Defectives 4 9 11 7 5 4 5 2 2 4
Lot No. 11 12 13 14 15 16 17 18 19 20
No. of Defectives 3672243957
Set up an appropriate control chart and comment on the state of control. 10
ii) Describe the procedure of the Chi-square test of goodness of fit. 5
_________________
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