Name of the Organisation : Department Of Economics,North-Eastern Hill University, Shillong
Exam : MA/MSc Question Papers
Subject : Techniques of Statistical Analysis
Year : 2015
Document Type : Model & Past Question Papers
Website : https://www.nehu.ac.in/
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Techniques of Statistical Analysis Question Paper :
Full Marks: 75;
Time: 3 hours
** The figures in the margin indicate full marks for the questions
** Answer five questions, selecting at least one from each Credit
Related : North-Eastern Hill University MA/MSc Macroeconomic Analysis-II Question Paper :www.pdfquestion.in/13319.html
CREDIT – I :
1. (a) Examine critically the different schools of thought on probability 8
(b) Derive the formulae of variance under the binomial probability distribution. 4
(c) A husband and wife appear in an interview for two vacancies in the same post. The probability of husband getting selected is 1/7 whereas that of wife is 1/5. What is the probability that (i) both of them will be selected; (ii) only one of them will be selected, and (iii) none of them will be selected? 3
2. (a) Write an explanatory note on Poisson distribution. 7
(b) A card is drawn from a well shuffled deck of playing cards. Find the probability of drawing a card which is neither a heart nor a king. 2
(c) A University has to select an invigilator from a list of 50 persons, 20 of them are women and 30 men, 10 of them speaking Khasi and 40 other languages, 15 of them being teachers and the remaining 35 are non-teaching staff. What is the probability of selecting a Khasi-speaking woman teacher? 3
(d) Is there any inconsistency in the statement that the mean of a binomial distribution is 20 and its standard deviation is 4? If no inconsistency is found, what shall be the values of p, q and n? 3
CREDIT – II :
3. (a) Use normal equations to estimate the increase in sales revenue expected from 15 per cent increase in advertisement expenditure: Percentage increase in advt. expenditure 1
3. (b) Derive the formula of rank correlation coefficient. 5
4. (a) Obtain the rank correlation coefficient between the variables X and Y from the following pairs of observed values
(b) Write a note on Coefficient of Determination. 5
CREDIT – III :
5. (a) Explain different components of a time series data. 7
(b) Assume a four-yearly cycle and estimate the trend by the method of moving average from the following data relating to the production of tea in India
CREDIT – IV :
7. (a) What is sampling distribution of sample mean? Explain the concept taking an example of drawing a sample of size of 2 with replacement from a population set 2,4,6,8. Also draw a histogram of sampling distribution of sample mean. 8+2
(b) Given a population with mean, 7 and standard deviation, 3.26, if a sample of size 10 is drawn with replacement, what is the probability that the sample mean is less than 6 but more than 4? 5
Techniques of Statistical Analysis 2014 :
Full Marks: 75;
Time: 3 hours
Note :
** The figures in the margin indicate full marks for the questions
** Answer five questions, selecting at least one from each Credit
Credit – I :
1. (a) Explain different approaches to the theory of probability using appropriate examples.
2. (a) Write short notes on the following:
(i) Normal probability distribution (ii) Poisson distribution
(b) There is a select panel of 4 BJP, 3 Congress, and 2 BJD members of Indian Parliament (MP). Find the number of committees of 5 MPs that can be constituted with 2 each from BJP and Congress and 1 from BJD members.
Credit – II :
3.(a) Rank correlation coefficient formula is a derivative of product moment formula. Examine.
(b) A set of paired data on X and Y has mean as 36 and 85 and that of standard deviation as 11 and 8 respectively. If the correlation coefficient between X and Y is 0.66, obtain (i) the regression of Y on X, (ii) the regression of X on Y and (iii) the value of X when Y=75.
Credit – III :
4. (a) Explain the Semi-Average method of estimating trend variations.
(b) The average rainfall in cm during 2006-2013 was recorded as under. Obtain (i) trend rainfall data using least square method, and (ii) cyclical relatives in rainfall.
6.(a) What do you mean by forecasting? Explain any two forecasting methods.
(b) Estimate the seasonal indices by the Ratio to Moving Average method from the following quarterly data for the period from 2010 to 2013:
Year Quarter :
I II III IV
2010 13 11 8 10
2011 15 10 9 12
2012 18 12 10 15
2013 20 15 11 18
CREDIT – IV :
7.(a) Develop the binomial probability rule.
(b) Four coins were tossed 200 times. The number of tosses showing 0, 1, 2, 3, and 4 heads were found distributed as under. Fit a binomial distribution to these observed results.
No. of heads 0 1 2 3 4
No. of tosses 15 35 90 40 20
8. (a) Derive the formula of standard deviation under binomial probability distribution.
(b) A survey undertaken by a charity organization to know the wages of women workers in two factories, A and B, published the following results in their annual reports. Given , test whether there is a significant difference in the average wages of women workers in the two factories.
Factory A Factory B :
Average wage of women workers (Rs.) 100 105
Standard deviation of wages 16 24
Number of workers 800 1600
(c) A random sample of 100 families with four children each disclosed the following data:
Female births 0 1 2 3 4
No. of families 5 25 40 20 10
Given , verify if these data are consistent with the hypothesis that male and female births are equally likely.