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Gauhati University BCom 3rd Sem CBCS

Business Statics Question Paper 2022

COMMERCE

(Honours Generic)

OPTION-A

Paper: COM-HG-3016

(Business Statistics)

Full Marks: 80

Time: Three hours

The figures in the margin indicate full marks for the questions.

Answer Question Nos. 1, 2, 3 and any four from the rest.

1. (a) Fill in the blanks: (any four) 1×4=4

(i) S.D. is independent of change of _______.

(ii) If r⌄xy is equal to 0.6, then r⌄yx is_______..

(iii) Regression coefficients have _____ sign.

(iv) Index number for base year is always taken as ____.

(v) A rise in prices before Diwali is an example of _______ variations of time series data.

(vi) The probability of occurrence of an event ranges from __ to ___.

(vii) Variance is equal to ____ of standard deviation.

(b) Select the correct answer: (any three) 1×3=3

(i) Which average is appropriate for computing average rate of growth?

(a) Arithmetic mean

(b) Median

(c) Geometric mean

(d) Harmonic mean

(ii) The frequence distribution is considered negatively skewed if the graph have a longer tail on

(a) left side

(b) right side

(c) both sides

(d) None of the above

(iii) Rank correlation is preferred if the nature of the data is

(a) quantitative data

(b) qualitative data

(c) Both (a) and (b)

(d) None of the above

(iv) Both regression coefficients cannot be

(a) greater than one

(b) smaller than one

(c) equal to one

(d) None of the above

(v) Index numbers are expressed in what form?

(a) Ratio

(b) Percenture

(c) Square

(d) None of the above

(c) Mean of a random variable X i

(a) E(X)

(b) E(X²)

(c) E ( )

(d) E(X²) - {E(X)}²

(c) Write True or False: (any two) 1 x 2 = 2

(i) For a number of positive values AM ≤ GM ≤ HM. (True)

(ii) In a normal distribution

Mean = Median = Mode (True)

(iii) Population characteristics are called statistic. (False)

(iv) Standard deviation can never be negative. (True)

(d) Mention the parameter(s) of Poisson distributuion. 1

2. Answer any five of the following questions: 2 x 5 = 10

(a) A student obtained :-

Is the data consistent ?

(c) Arithmetic mean of 8 numbers is 15. Afterward a new number 24 is added. What is the A.M. of 9 numbers ?

(d) Write two differences between census and sample survey.

(e) What is level of significance ?

(f) What do you understand dispersion ? by

(g) Two events A and B are mutually exclusive. If P(A)=⅕ and P(B)=⅓ , find the probability that at least one event will occur.

(h) What do you mean by price relative ?

(i) What should be the base year like in constructing index number ?

(i) What is null hypothesis ?

3. Answer any four of the following questions: 5×4=20

(a) What are the characteristics of an ideal average?

(b) In a distribution A.M. = 45, Median 48, Coefficient of skewness -0.4. Find the value of standard deviation and mode.

(c) What is scatter diagram ? How does it help us in studying the correlation between two variables?

(d) Mention the chief characteristics of normal distribution.

(e) Discuss the advantages of sample survey over census method.

(f) Write a note on usefulness of index number.

(g) Assuming the probability of a male 1/2 birth as find the probability that a family of 3 children will have

(i) one girl, and

(ii) at least one girl.

(h) Explain the concepts of type I and type II error of testing hypothesis. 2+4=6

4. (a) Calculate mean and coefficient of variation from the following data: 2+4=6

(b) What is skewness ? Explain different types of skewness. 4

5. (a) What is Karl Pearson's coefficient of correlation ? What does it measure? Interpret the following values of coefficient of correlation : r=-1, r=0, r=1. 4

b) Estimate the two regression equations from the following data: 5+1=6

Also estimate X, if Y= 20.

6.(a) Define: 2+2=4

(i) Random Experiment

(ii) Trial and Event

(b) A meteorologist has forecast the probability of rains on Monday, Tuesday and Wednesday

as 0.6, 0.5 and 0.3 respectively. Assuming that the weather from day to day is independent,

what is the probability that it will rain at least once in these three days ?

7. (a) What is Poisson distribution? Give two examples of poisson distribution. 2+2= 4

(b) If three coins are tossed at a time, find expectation and variance of the number of heads. 6

6.(a) Six coins are tossed simultaneously. What is the probability of getting (i) 2 heads, and (ii) more than 2 heads. 6

(b) Explain the importance of normal distribution in statistics.

9. (a) Calculate the trend values by using least square method and estimate the sales of 2022 from the following data : 5+1=6

(b) What is index number ? What are various types of index number ? 1+3=4

10.(a) What is time series ? What is the purpose of time series analysis ? 1+3=4

(b) Calculate index numbers from the following data using Laspeyre's, Paasche's and Fisher's formulae : 2+2+2=6

11. (a) What is test of significance ? Discuss various steps associated with test of significance. 6

(b) Explain the concept of (i) point estimation, and (ii) interval estimation.

12. (a) What is sampling distribution ? Explain. 5

(b) What is simple random sampling ? Discuss advantages and disadvantages of this method. 5

13. (a) What is dispersion ? Why is S.D. called the best measure of dispersion ? 5

b) From the following information, calculate Karl Pearson's coefficient of correlation: 5

∑ 𝑋=100, ∑ 𝑋=150,n=10

∑(𝑋 − 10)² =180, ∑(𝑌 − 15)²=215,

∑(𝑋-10) (𝑌 − 15)=60

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