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2022
BUSINESS STATISTICS
(GE) (GA)
Paper: 3.1
(Business Statistics)
Full Marks: 80
Time: 3 hours
The figures in the margin indicate full marks for the questions.
1. Answer the following questions as directed: 1×10=10
(a) At which point the two cumulative frequency curves intersect each other?
(b) Write one use of mode.
(c) In inclusive classification the class limits and the class boundaries of a class are the same. (Write true or false)
(d) Select the correct answer : If 'A' is any event, then
(i) P(A)>1
(ii) O <P(A)<1
(iii) P(A) < O
(iv) O<P(A) > 1
(e) If E(CX) = CE(X) then what is the value of V(CX) where C is any constant.
(f)If r = 0 the two lines of regression are
(i) Parallel
(ii) Coincident
(iii) Perpendicular to each other
(iv) None of the above
(Choose the correct one)
(g) What type of correlation is present in this situation ? Price and demand of a commodity'.
(h) Drobish-Bowley's index number is J the_____of Laspeyre's and Paasche's index number. (Fill in the blank)
(i)'n' and 'p' are the only Parameters of Binomial distribution. (Write true or false)
(j) The level of significance is associated with______. (Fill in the blank)
Also Read
Answer any five questions: 2×5-10
(a) Find the Geometric mean (G.M.) of 3.2 and 0.2.
(b) Write two different characteristics of an index number.
(c) Mention any two properties of regression co-efficient.
(d) Define mutually exclusive event with example.
(e) Find E(X)
X : 0 1 2 3
P(X): ¼ ¼ ¼ ¼
(f) If E(X)=4 and V(X)=5, find the value of E(2X+3) and V (2x+3).
3. Answer any four questions of the following: 5×4-20
(a) Write a note on the limitations of statistics. 5
(b) Show that for a set of positive values
AM≥ GM > HM. 5
(c) Show that variance (or standard deviation) is affected only by change of scale, not by change of origin. 5
(d) Define correlation coefficient. The correlation coefficient of two variables x and y is 0.4 and their co-variance is 12. If the standard deviation of y be 5, find the variance of x. 1+4-5
(e) What are the different components of time series? Calculate 3-yearly moving average from the following data: 5
Year: . 1999 2000 2001 2002 2003 2004 2005
Production: 40 45 46 42 47 49 46
('000 tons)
(f) The Probability that a contractor will get a plumbling contract is 2/3 and the Probability that he will not get an electric contract is 5/9. If the probability of getting any one contract is 4/5, what is probability that he will get both the contracts ? 5
Answer any four questions: 10×4-40
(a) Define median. Calculate arithmetic mean (A.M.) and standard deviation (S.D.) for the following distribution. 2+3+5=10
Marks : 0-10 10-20 20-30 30-40 16 40-50 50-60
No. of Students: 6 5 8 16 7 6
(b)(i) Distinguish between fixed base and chain base index numbers. Discuss their relative advantages and disadvantages. 5
(ii) Show that Fisher's index number satisfies both Time reversal test (TRT) as well as Factor reversal test (FRT). 5
(c) (i)Define Cost of living index number (CLIN). The following table gives the index numbers for different groups of items with their respective weights for 2005 (base year=2000):
Group: Food Clothing Fuel Rent OthersGroup index no.: 525 325 240 180 200
Group weight ; 40 16 15 20 9
(ii) Calculate the overall cost of living index number..
(ii) Mr. Boro got a salary of Rs. 8,500 in 2000. Determine how much he should have to receive as salary in 2005 to maintain the same standard of living as in 2000. 2+6+2=10
(d)(i)Fit a straight line trend of the following time series data and estimate the likely Profit for the year 2004. 5
Year:1997 1998 1999 2000 2001 2002 2003
Profit:60 72 75 65 80 85 95
(Rs. In lakh)
(ii) A problem is given to five students A, B, C, D and E. Their respective chances of solving it are ½,⅓,¼,¼ and ¹/5 . What is the probability that at least one of the students solves the problem, if they try it independently ? 5
(e)(i)Define skewness. Of a certain distribution, the Karl Pearson's co efficient of skewness is 0.32, Standard deviation is 6.5 and mean is 29.6. Find the median and the mode of the distribution. 2+2+2=6
(ii)Define Null-hypothesis and Alternative hypothesis associated with test of significance. 2+2=4
(f)(i) From the following results, obtain the two regression equations and estimate the yield when the rainfall is 29 cm. 5
Rainfall (cm) Yield (kg)
Mean:. 26.7 508.4
Standard deviation: 4.6 36.8
Correlation co-efficient between yield and rainfall is 0.52.
(ii) Define Poisson distribution. A random variable X follows Poisson distribution with Parameter 4. Find the Probability that X sdi ei is assumes values less than 2. orit too (Given e-⁴ = 0.01x83). 2+3-5
(g) Write short notes on (any two) 5x2 = 10
(i) Concept of Kurtosis $8.0
(ii) Multiple and Partial Correlation as
(iii) Census Vs Sampling method
(iv) Errors in testing hypothesis.
(h) (i)Write down the Probability mass function (Pmf) of Binomial distribution. Under what condition Binomial distribution tends to Poisson distribution ? Write two properties of Binomial distribution. 10.
(ii) A normal curve has overlinex = 20 sigma = 10 .Find the area between X¹ = 15 and X² = 40. 5
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