Exercise

Exercise 14 - Probability Distribution of the Spread

What does the central limit theorem tell us about the distribution of the differences between the pollster averages, \(\bar{Y}_2 - \bar{Y}_1\)?

50 XP

The central limit theorem cannot tell us anything because this difference is not the average of a sample.

Because \(Y_{ij}\) are approximately normal, the averages are normal too.

If we assume \(N_2\) and \(N_1\) are large enough, \(\bar{Y}_2\) and \(\bar{Y}_1\), and their difference, are approximately normal.

These data do not contain vectors of 0 and 1, so the central limit theorem does not apply.