University Of Pune Question Paper
M.Com. (Semester – III) Examination, 2013
BUSINESS STATISTICS (Old)
Time : 3 Hours Max. Marks : 100
N.B. : 1) All questions are compulsory.
2) Figures to the right indicate full marks.
3) Use of statistical tables and calculator is allowed.
4) Symbols have their usual meanings.
1. Attempt any four of the following : 20
a) Define the following terms :
a) Level of significance
b) Binomial distribution
c) Poisson distribution
d) Test of hypothesis
e) Probability distribution of discrete random variable
b) Explain the procedure of large sample test of population mean.
c) State inter-relationship between Binomial, Poisson and Normal Distribution.
d) A random variable X has following probability distribution :
X 01 2 3 4 5
P(X=x) 0.1 0.1 0.2 0.3 0.2 0.1
Find mean and variance of X.
e) The average number of trucks arriving on a day at a truck depot is known to
be 12. What is the probability that on a given day fewer than 9 trucks arrive
at this depot ? (Given e– 12 = 0.000006).
f) A random sample of 18 pairs of observations from a normal population gives
a correlation of 0.46. Is it likely that the variables in the population are
uncorrelated ?
(Use 5% L.O.S., given t16 = 2.12, t17 = 2.11, t18 = 2.10).
Seat
No.
[4370] – 320 -2-
2. Attempt any four of the following : 20
a) What do you mean by random variable ? Explain the difference between
discrete and continuous random variable with an illustration.
b) A random variable X has following probability distribution :
X 01 2 3 4 5
P(X=x) K 4K 5K 7K 2K K
Find
i) K
ii) ≤< )3X1(P
iii) ≥ )2X(P .
c) Explain process control and product control.
d) A group of 50 men and 60 women was asked to indicate their preference
between two brands of perfume revealed the following results :
Attribute Brand A Brand B
Men 20 30
Women 10 50
Test the hypothesis that the performance for particular brand of perfume is
not related to sex, at 5% L.O.S.
Given .3 81 .5, 99 .7, 81 2
3
2
2
2
1 =χ=χ=χ .
e) A production department of a company knows from the past experience that
there is 30% chance of finding defect. If 10 units of the product are examined,
find probability that not more than 1 defective product is found.
f) Explain the concept of acceptance sampling.
-3- [4370] – 320
3. Attempt any four of the following : 20
a) The ability of breaks of two new types of cars was tested by driving the new
cars at the speed of 60 miles per hour and then applying the breaks. The
distances (in inches) required to stop the cars were noted. The result were
as follows :
Type of the car I II
No. of cars tested 12 15
Mean distance (in inches) 7.8 9.6
S.D. of distance 2.2 3.5
Is the difference in their average distance significant ? Use 5% level of
significance.
(Given t25 = 2.06, t26 = 2.056, t27 = 2.052)
b) Explain method of moving averages to measure trend in time series.
c) Explain the procedure of 2 χ test for goodness of fit.
d) Find 5-yearly moving average for the following data on sales.
Year 2000 01 02 03 04 05 06 07 08 09
Sales 50 82 65 86 70 52 90 65 87 43
e) Explain working of single sampling plan.
f) Fit a trend line to the following data by least square method. Also obtain
production for the year 2005.
Year 1998 1999 2000 2001 2002
Production 12 20 28 32 50
4. Attempt any two of the following : 20
a) If X → N (100, 82), find
i) P (X >108)
ii) P (X < 110)
iii) P (88 < X < 108)
E (Y) and Var (Y), where Y = 3X + 5.
b) I)Suppose X → B (n, p)
i) If E(X) = 6, Var (X) = 4.2, find n and p
ii) If E(X) =10, n = 25, find p, Var (x) and SD of X.
[4370] – 320 -4-
II) Classify the following random variable as discrete or continuous :
i) Number of two wheelers passing through bridge during 9 a.m. to 11. a.m.
ii) Life of an electric bulb.
iii) Number of students present in a class on a day.
iv) A coin is tossed till head appears.
v) Weight of student.
c) The following data relates to weights of 10 persons before joining a health
club and after 6 months from joining it. Test whether there is a significant
change in the weights after 6 months from joining the club. (Use 1% l.o.c..
given t9 = 3.25, t10 = 3.16)
Participant No. 1 2 3 4 5 6 7 8 9 10
Weight before
joining club 120 125 115 130 123 119 122 127 128 118
Weight after 6
months 111 114 107 120 115 112 112 120 119 112
5. Attempt any two of the following : 20
a) Draw P chart for following data of number of defectives in 10 samples of
size 50 each and comment on the result.
8, 6, 5, 7, 2, 5, 3, 8, 4, 4,
b) What do you mean by time series ? Explain different components of time
series.
c) Below are given the means and ranges of 10 samples of size 5 each taken
from a certain production process at regular intervals.
14.2 13.9 15.5 12.1 14.1 13.2 12.9 13.5 13.1 12.8
R 2.0 2.5 2.8 2.5 3.0 1.9 2.1 3.9 3.1 2.1
Given n = 5, D3 = 0, D4 = 2.115, A2 = 0.577, Draw X chart, R chart and
comment.
______________
B
M.Com. (Semester – III) Examination, 2013
BUSINESS STATISTICS (Old)
Time : 3 Hours Max. Marks : 100
N.B. : 1) All questions are compulsory.
2) Figures to the right indicate full marks.
3) Use of statistical tables and calculator is allowed.
4) Symbols have their usual meanings.
1. Attempt any four of the following : 20
a) Define the following terms :
a) Level of significance
b) Binomial distribution
c) Poisson distribution
d) Test of hypothesis
e) Probability distribution of discrete random variable
b) Explain the procedure of large sample test of population mean.
c) State inter-relationship between Binomial, Poisson and Normal Distribution.
d) A random variable X has following probability distribution :
X 01 2 3 4 5
P(X=x) 0.1 0.1 0.2 0.3 0.2 0.1
Find mean and variance of X.
e) The average number of trucks arriving on a day at a truck depot is known to
be 12. What is the probability that on a given day fewer than 9 trucks arrive
at this depot ? (Given e– 12 = 0.000006).
f) A random sample of 18 pairs of observations from a normal population gives
a correlation of 0.46. Is it likely that the variables in the population are
uncorrelated ?
(Use 5% L.O.S., given t16 = 2.12, t17 = 2.11, t18 = 2.10).
Seat
No.
[4370] – 320 -2-
2. Attempt any four of the following : 20
a) What do you mean by random variable ? Explain the difference between
discrete and continuous random variable with an illustration.
b) A random variable X has following probability distribution :
X 01 2 3 4 5
P(X=x) K 4K 5K 7K 2K K
Find
i) K
ii) ≤< )3X1(P
iii) ≥ )2X(P .
c) Explain process control and product control.
d) A group of 50 men and 60 women was asked to indicate their preference
between two brands of perfume revealed the following results :
Attribute Brand A Brand B
Men 20 30
Women 10 50
Test the hypothesis that the performance for particular brand of perfume is
not related to sex, at 5% L.O.S.
Given .3 81 .5, 99 .7, 81 2
3
2
2
2
1 =χ=χ=χ .
e) A production department of a company knows from the past experience that
there is 30% chance of finding defect. If 10 units of the product are examined,
find probability that not more than 1 defective product is found.
f) Explain the concept of acceptance sampling.
-3- [4370] – 320
3. Attempt any four of the following : 20
a) The ability of breaks of two new types of cars was tested by driving the new
cars at the speed of 60 miles per hour and then applying the breaks. The
distances (in inches) required to stop the cars were noted. The result were
as follows :
Type of the car I II
No. of cars tested 12 15
Mean distance (in inches) 7.8 9.6
S.D. of distance 2.2 3.5
Is the difference in their average distance significant ? Use 5% level of
significance.
(Given t25 = 2.06, t26 = 2.056, t27 = 2.052)
b) Explain method of moving averages to measure trend in time series.
c) Explain the procedure of 2 χ test for goodness of fit.
d) Find 5-yearly moving average for the following data on sales.
Year 2000 01 02 03 04 05 06 07 08 09
Sales 50 82 65 86 70 52 90 65 87 43
e) Explain working of single sampling plan.
f) Fit a trend line to the following data by least square method. Also obtain
production for the year 2005.
Year 1998 1999 2000 2001 2002
Production 12 20 28 32 50
4. Attempt any two of the following : 20
a) If X → N (100, 82), find
i) P (X >108)
ii) P (X < 110)
iii) P (88 < X < 108)
E (Y) and Var (Y), where Y = 3X + 5.
b) I)Suppose X → B (n, p)
i) If E(X) = 6, Var (X) = 4.2, find n and p
ii) If E(X) =10, n = 25, find p, Var (x) and SD of X.
[4370] – 320 -4-
II) Classify the following random variable as discrete or continuous :
i) Number of two wheelers passing through bridge during 9 a.m. to 11. a.m.
ii) Life of an electric bulb.
iii) Number of students present in a class on a day.
iv) A coin is tossed till head appears.
v) Weight of student.
c) The following data relates to weights of 10 persons before joining a health
club and after 6 months from joining it. Test whether there is a significant
change in the weights after 6 months from joining the club. (Use 1% l.o.c..
given t9 = 3.25, t10 = 3.16)
Participant No. 1 2 3 4 5 6 7 8 9 10
Weight before
joining club 120 125 115 130 123 119 122 127 128 118
Weight after 6
months 111 114 107 120 115 112 112 120 119 112
5. Attempt any two of the following : 20
a) Draw P chart for following data of number of defectives in 10 samples of
size 50 each and comment on the result.
8, 6, 5, 7, 2, 5, 3, 8, 4, 4,
b) What do you mean by time series ? Explain different components of time
series.
c) Below are given the means and ranges of 10 samples of size 5 each taken
from a certain production process at regular intervals.
14.2 13.9 15.5 12.1 14.1 13.2 12.9 13.5 13.1 12.8
R 2.0 2.5 2.8 2.5 3.0 1.9 2.1 3.9 3.1 2.1
Given n = 5, D3 = 0, D4 = 2.115, A2 = 0.577, Draw X chart, R chart and
comment.
______________
B
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