  In this paper,our main focus is to obtain an asymptotic bound on the family
wise error rate (FWER) for Bonferroni-type procedure in the simultaneous
hypotheses testing problem when the observations corresponding to individual
hypothesis are correlated. In particular, we have considered the sequence of
null hypotheses H_{0i} : X_i follows N(0,1) , (i=1,2,....,n) and equicorrelated
structure of the sequence (X_1,....,X_n). Distribution free bound on FWER under
equicorrelated setup can be found in Tong(2014). But the upper bound provided
in Tong(2014) is not a bounded quantity as the no. of hypotheses(n) gets larger
and larger and as a result,FWER is highly overestimated for the choice of a
particular distribution (e.g.- normal). In the equicorrelated normal setup, we
have shown that FWER asymptotically is a convex function (as a function of
correlation (rho)) and hence an upper bound on the FWER of Bonferroni-(alpha)
procedure is alpha(1-\rho).This implies,Bonferroni's method actually controls
the FWER at a much smaller level than the desired level of significance under
the positively correlated case and necessitates a correlation correction.
