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Suppose X and Y are two populations with Normal Distributions with different means and identical standard deviation. Suppose sample A and sample B are random

Suppose X and Y are two populations with Normal Distributions with different means and identical standard deviation. Suppose sample A and sample B are random samples of size 30 from X and Y respectively. What do you think is the relationship between standard deviation and whether NULL hypothesis that "observed difference between sample A and sample B is due to chance" can be rejected?

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