CSS past paper

CSS Statistics Past Paper 2024

CSS Statistics 2024 carries 100 marks over 3 hours. It has 7 questions.

Marks: 100
Time: 3 hours
Questions: 7

Years

How to attempt: Attempt FOUR questions in all by selecting TWO Questions each from SECTION. ALL questions carry EQUAL marks.

Questions

Question 1 (Part I) is the paper's MCQs, which are not reproduced here.

SECTION-A

Q. 2
(20)
- (a)
  What methods you employed in the collection of statistical data when the field of inquiry is (i) small, (ii) fairly large and (iii) very large, if you are to pay due regard to accuracy, labor, cost and time.
  (10)
- (b)
  If $\log_{e} x$ is normally distributed with $\mu = 1$ and $\sigma^{2} = 4$ , find P( ½ < x < 2), given $\log_{e} 2$ = 0.693.
  (10)
Q. 3
In a certain experiment to compare two types of sheep food A and B, the following results of increase in weights were observed:
(20)
Sheep No. 1 2 3 4 5 6 7 8
Food A 49 53 51 52 47 50 52 53
Food B 52 55 52 53 50 54 54 53
- (i)
  Assuming that the two samples of sheep are independent, can we conclude that food B is better than food A?
  (10)
- (ii)
  Examine the case when the same set of eight sheep was used in both the foods.
  (10)
Q. 4
(20)
- (a)
  An urn contains 10 white and 3 black balls. Another urn contains 3 white and 5 black balls. Two balls are transferred from first urn and placed in the second and then one ball is taken from the latter. What is the probability that it is a white ball?
  (10)
- (b)
  Differentiate between Poisson distribution and Poisson process. Give examples in each case.
  (10)
Q. 5
(20)
- (a)
  Given the following population distribution:
  (10)
  x 1 2 3 4
  f(x) 1/7 3/7 2/7 1/7
  Find the sampling distribution of the mean if a sample of three numbers is taken without replacement. How does the variance of the sampling distribution compare with the population variance?
- (b)
  A random sample of size n = 100 is taken from a population having a mean of 20 and a standard deviation of 5. The shape of the population distribution is unknown.
  (10)
  - (i)
    What can you say about the sampling distribution of the sample mean?
  - (ii)
    Find the probability that sample mean exceeds 20.75.

SECTION-B

Q. 6
(20)
- (a)
  A confidence interval is constructed from a random sample of size n = 50, for the mean yield of a normal population which has $\sigma$ = 21 tons. The limits for the interval are 866.11 and 875.89 tons. What confidence co-efficient was used?
  (10)
- (b)
  How will you construct confidence interval for difference of means of a normal population?
  (10)
Q. 7
(20)
- (a)
  Describe the main steps involved in the construction of index numbers of wholesale prices.
  (10)
- (b)
  The prices and quantities of three commodities during 2002 and 2004 are given below:
  (10)
  Commodity Prices ( Rs. Per 40 Kilogram) Quantities Produced (Kilograms)
  2002 2004 2002 2004
  A 3.95 4.25 9,675 10,436
  B 34.80 38.94 78 83
  C 61.56 59.70 118 116
  Compute the Marshall-Edgeworth and the Walsh’s price index numbers for 2004, using 2002 as the base period.
Q. 8
(20)
- (a)
  Describe a Randomized Complete Block Design experiment and give its layout.
  (10)
- (b)
  In a Randomized Complete Block Design, in each of four blocks I, II, III, IV, four varieties of wheat A,B, C, D are grown in the layout given below and the yields are also indicated therein:
  (10)
  I B 27 A 17 C 15 D 25
  II A 28 D 22 B 26 C 16
  III D 14 C 11 A 22 B 25
  IV C 18 B 18 D 19 A 17
  - (i)
    Perform the analysis of variance to test at 0.05 significance level, the difference in the yields of varieties and in blocks.
  - (ii)
    What would be the result if no blocking had been done. i.e., if we consider it as a completely randomized design?

Commodity	Prices ( Rs. Per 40 Kilogram)		Quantities Produced (Kilograms)
A	3.95	4.25	9,675	10,436
B	34.80	38.94	78	83
C	61.56	59.70	118	116

Part-II is to be attempted on the separate Answer Book.
Attempt FOUR questions in all by selecting TWO Questions each from SECTION. ALL questions carry EQUAL marks.
All the parts (if any) of each Question must be attempted at one place instead of at different places.
Write Q. No. in the Answer Book in accordance with Q. No. in the Q.Paper.
No Page/Space be left blank between the answers. All the blank pages of Answer Book must be crossed.
Extra attempt of any question or any part of the question will not be considered.
Use of Calculator is allowed.

Sheep No.	1	2	3	4	5	6	7	8
Food A	49	53	51	52	47	50	52	53
Food B	52	55	52	53	50	54	54	53

Commodity	Prices ( Rs. Per 40 Kilogram)		Quantities Produced (Kilograms)
	2002	2004	2002	2004
A	3.95	4.25	9,675	10,436
B	34.80	38.94	78	83
C	61.56	59.70	118	116

I	B 27	A 17	C 15	D 25
II	A 28	D 22	B 26	C 16
III	D 14	C 11	A 22	B 25
IV	C 18	B 18	D 19	A 17

x	1	2	3	4
f(x)	1/7	3/7	2/7	1/7