# Difference Between Two Population Means

Two samples are said to be paired or matched samples when for each data value collected from one sample there is a corresponding data value collected from the second sample, and both these data values are collected from the same source. As another example of paired samples, suppose an agronomist wants to measure the effect of a new brand of fertilizer on the yield of potatoes. To do so, he selects 10 pieces of land and divides each piece into two portions. Then he randomly assigns one of the two portions from each piece of land to grow potatoes without using fertilizer (or using some other brand of fertilizer). The second portion from each piece of land is used to grow potatoes with the new brand of fertilizer. Thus, he will have 10 pairs of data values. Then, using the procedure to be discussed in this article, he will make inferences about the difference in the mean yields of potatoes with and without the new fertilizer. The question arises, why does...

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