Inferring Population Difference

The growth of the world economy

Did the world economy grow faster in 1990 than in 1960? The question asks us to find out whether the average economic growth in 1990 remained the same as in 1960 or not. The idea behind this question is to learn to use the difference between two samples (one for 1960, the other for 1990) to estimate and predict the difference between two populations (one for 1960, the other for 1990).

Infer population difference from sample difference

Suppose $\mu_{1960}$ and $\mu_{1990}$ represent the average economic growth rates in the populations of 1960 and 1990, respectively. The answer to the question is $\mu_{1960}$ − $\mu_{1960}$. . Since we don’t have the population data, we can only use the difference between the two sample means, $\bar{y}_{1960}$ − $\bar{y}_{1960}$, based on the pwt7g data, to estimate the difference between the two population means.

Using the pwt7g data, we compute the following sample statistics: