Suppose Xi are N (, 2) for i = 1,...,n, where n is large. We use X

Suppose Xi are N (µ, σ2) for i = 1,...,n, where n is large. We use X to estimate µ. True or false and explain:

(a) If the Xi are independent, then X will be around µ, being off by something like s/√n; the chance that |X − µ| < s/√n is about 68%.

(b) Even if the Xi are dependent, X will be around µ, being off by something like s/√n; the chance that |X − µ| < s/√n is about 68%.

What are the implications for applied work? For instance, how would dependence affect your ability to make statistical inferences about µ?

(Notation: X and s2 were defined in question 7.)