Critical Comparison of Some Interesting Statistics in Case of Mean of Normal Population by Considering ‘Variance’ as Nuisance Parameter Using Bootstrapping Technique-II

The objective of this paper is to empirically estimate the confidence intervals and compare some important statistics with regard to the mean of normal population by considering variance as ‘nuisance parameter', in the sense of Khan (1969). The paper uses the method of constructing a sequential procedure for obtaining fixed-width confidence intervals of prescribed coverage probability, as developed in Prasad and Sarma (2009). For this, the bootstrapping technique introduced by Efron and Tibshirani (1993), which is the latest simulation technique for estimating confidence intervals of parameters of a population, is used. Numerical results are obtained using the program developed in C by varying different statistics involved. By taking initial sample size as n0 = 10, results are obtained for the following statistics: (1) Confidence intervals for the mean; (2) Average sample number; (3) Standard error of N; and (4) Coverage probabilities using bootstrap method, which are then compared to that of the standard Monte Carlo method