Veer Narmad South Gujarat University 2010 M.Com Commerce Advaced Statistics : - I, - - Question Paper
RA-3357 M. Com. (Part - I) Examination March / April - 2010 Advanced Statistics : Paper - I
Time : 3 Hours] 00
[Total Marks : 70
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Name of the Examination :
M. COM. (PART - 1)
Name of the Subject:
ADVANCED STATISTICS - 1
-Section No. (1,2,.....): NIL
Student's Signature
-Subject Code No.
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Instructions : (1) As per the Instruction no. 1 of page no. 1.
(2) Figures to the right indicate full marks of the questions.
1 (a) Explain the method of moments for the estimation 7 of the parameter.
(b) Find 98% confidence interval for the mean of a 7
normal distribution, if a = 2 and if a sample of size 8 gave the values 9, 14, 10, 12, 7, 13, 11, 12.
1 (a) Define consistent estimator. Explain the method of 7 moments for the estimation of parameter.
(b) Obtain maximum likelihood estimator from a random 7 sample taken from the binomial distribution
where, x = 0,1,2,......,n p = l-q 0<p<l
2 (a) State Neyman-Pearson Lemma, state its uses. 6
(b) Explain with illustration the concept of confidence 8
interval, state its uses. Obtain (l-a)l00% confidence
interval for mean |i of normal population.
2 (a) Explain following terms : 6
(1) Best critical region
(2) Power of test
(3) Null hypothesis and alternative hypothesis.
(b) A random sample is taken from a probability 8
distribution f{x,p) = px(l-pf x x = 0,1, 0<p<l, find the best critical region of size a to test Hq : p = against H1 : p = %.
(a) Obtain probability density function of hyper geometric distribution.
(b) Define Laplace distribution. Obtain its characteristic function.
7
(a) Define log normal distribution. If a2j then obtain the distribution of ex.
Xl
(b) Find the distribution of (i) Xl X2 and (ii) for
X- ~ Nhi- a- = 1, 2 are independent.
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Explain Kendall - T test. The following are the final examination marks of three groups of students by three different methods | ||||||||||||||||||||||||
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(a)
(b)
6
8
Use Krushkal-Wallis test at the 5% level of significance to test the null hypothesis that there is no difference between three methods.
Explain Kolmogorov-Smirnov test.
(a)
(b)
6
8
10 observations are taken from a continuous distribution given below :
8.0, 5.4, 5.9, 2.3, 3.6, 7.2, 4.5, 4.4, 3.1, 3.0.
If the population mean is 11, test the hypothesis Hq : |i = 3 against H1 : |i 3 by using Wilcoxen Sign Rank test at level a = 0.05- Give your conclusion.
5 Write short notes : (any two) 14
(1) Krushkal - Wallis test
(2) Interval estimation and confidential limits
(3) Parametric and Non-parametric test.
RA-3357] 4 [ 300 ]
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| Earning: Approval pending. |
