Loyola College B.Sc. Statistics April 2009 Computational Statistics Question Paper PDF Download

     LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

YB 27

FIFTH SEMESTER – April 2009

ST 5503 – COMPUTATIONAL STATISTICS

 

 

 

Date & Time: 04/05/2009 / 1:00 – 4:00       Dept. No.                                          Max. : 100 Marks

 

 

 

Answer any THREE questions. Each carries 34 marks.

  1. 1. (i) Find seasonal variations by ratio-to-trend method from the data given below:
Year 1st Quarter 2nd Quarter   3rd Quarter 4th Quarter
1999 30 40 36 34
2000 34 52 50 44
2001 40 58 54 48
2002 54 76 68 62
2003 80 92 86 82

 

 

 

 

 

 

(ii) Assuming a four yearly cycle, calculate the trend by the method of moving averages from the following data relating to production of tea:

 

Year 1961 ‘62 ‘63 ‘64 ‘65 ‘66 ‘67 ‘68 ‘69 ‘70
Production 464 515 518 467 502 540 557 571 586 612

 

  1. In a population with N = 4, the Yi values are 1, 2, 3, 4. Enlist all possible samples of size n = 2, with SRSWOR and verify that E (s2) = S2.

 

  1. 3. (i) A sample of 30 students is to be drawn from a population consisting of 300 students belonging to two colleges A and B. The means and standard deviations of their marks are given below:
Total no. of students(Ni) Mean Standard deviation(σi)
College A 200 30 10
College B 100 60 40

 

 

 

How would you draw the sample using proportional allocation technique? Hence obtain the variance of estimate of the population mean and compare its efficiency with simple random sampling without replacement.

 

(ii) An institution which gives coaching for students planning to appear for a competitive exam in English wishes to test the efficacy of its coaching programme in improving this course. Then pre-coaching and post-coaching tests are conducted. The following data were obtained from a sample of 15 students who were subjected to both the tests:

Pre-coaching score: 56, 47, 61, 79, 53, 68, 72, 85, 59, 61, 70, 53, 68, 77, 83

Post- coaching score: 97, 53, 63, 82, 53, 64, 83, 89, 66, 63, 70, 50, 60, 84, 89

Carry out the relevant tests and report your findings.

 

 

 

  1. (i) Calculate Laspeyre’s, Paasche’s, Bowley’s and Fisher’s Ideal index from the following data.

 

Commodity Price

(2004)

Value

(2004)

Price

(2005)

Value

(2005)

Bricks 10 100 8 96
Sand 16 96 14 98
Timber 12 36 10 40
Cement 15 60 5 25

 

 

(ii) Calculate chain based index numbers from the price of the following three commodities:

Commodity 1999 2000 2001 2002 2003
Wheat 4 6 8 10 12
Rice 16 20 24 30 36
Sugar 8 10 16 20 24

 

 

 

 

 

 

  1. (i) Suppose that a group of 100 men received a flu vaccine and five of them died within the next one year. It is known that the probability of a man who did receive the vaccine will die within the next year is 0.02. Given this information, is the above mentioned event unusual or can this death rate be expected normally?

 

(ii) A new drug is to be tested for the treatment of patients with unstable angina. The effect of this drug is unknown. The following changes in the heart rate were observed among 20 patients: 4, -2, -3, 8, -3, -4, 2, 0, 1, 6,   -4, -7, 3, -3, 0, 5, 6, 3, -4, -2. The experimenter would like to know whether the drug induces a significant change in heart rate after 48 hours of administration.

 

 

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