**INTERNATIONAL INSTITUTE OF MANAGEMENT & TECHNICAL STUDIES**

**Subject Name: ****Quantitative technique in Management**

**Section A ****Attempt the following questions(2*10)** :

(a) Define unbiased and consistent estimator.

(b) Define sample proportion. Obtain its standard error.

(c) Give an example of an estimator which is consistent buunbiased.

(d) Explain Type – I and Type – II errors.

(e) Define a maximum likelihood estimator.

(f) Distinguish between level of significance of p-value.

(g) Define a consistent estimator

(h) Let X1 ……, Xn, be independent random variables such that Xifollows Poisson distribution with parameter ai, c = 1, …., n. Obtain the sampling distribution of: Y =∑

(i) State the uses of the result that sample mean and sample variance of a random sample from a normal distribution are independently distributed

(j) Define an F-Statistic. Derive its probability density function

** Section B****(Attempt any 4 questions.All carry equal marks)**

(1) Define a chi-square random variable. Derive its probability function

(2) What are the applications of chi-square statistic?

(3) Let X1… Xn be a random sample from a binomial distribution with parameter n and p. Explain a large sample test for testing a atleal value of p. Also construct 100 (1 – % confidence Interval for p 7.

(4) Define a goodness of fit problem. Discuss chi-square test of goodness of fit. (b) Explain a test for testing the independence of two attributes each at two levels. Also explain the Yate’s correction.

(5)Let X1…. Xm and Y1…. Yn, be random samples from N( ) and N( ) Propose a test for testing Ho – against all the three types of alternatives when , is unknown. Also construct 100 (1- ) percent confidence interval for the difference – –

(6)Explain a test for testing the significance of sample correlation coefficient

(7) Discuss a large sample test for testing the hypothetical value of population correlation coefficient.