We have a random variable X1 defined on Population 1.  X1 has a mean value of 52 with a population standard deviation of 3.  The random variable X2 is defined on Population 2 and X2 has a mean value of 50 with a population standard deviation of 4.  We obtain a random sample of 625 elements from Population 1, and independently we obtain a random sample of 625 elements from Population 2.  Find the probability that the difference in the sample averages X1- X2 is at least 2.5.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.