| Abstract
| - Let X 1,...,X n 1 be a random sample from a population with mean µ1 and variance $\sigma_1^2$, and X 1,...,X n 1 be a random sample from another population with mean µ2 and variance $\sigma_2^2$ independent of { X i,1 ≤ i ≤ n 1}. Consider the two sample t-statistic $ T={{\bar X-\bar Y-(\mu_1-\mu_2)} over \sqrt{s_1^2/n_1+s_2^2/n_2}}$. This paper shows that ln P(T ≥ x) ~ -x²/2 for any x := x(n 1,n 2) satisfying x → ∞, x = o(n 1 + n 2) 1/2 as n 1,n 2 → ∞ provided 0 < c 1 ≤ n 1/n 2 ≤ c 2< ∞. If, in addition, E|X 1| 3< ∞ , E|Y 1| 3< ∞ , then $\frac{P(T \geq x)}{1-\Phi(x)} \to 1 $ holds uniformly in x ∈ (O,o((n 1 + n 2) 1/6)) .
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