To illustrate Galton’s thesis of regression to the mean, the British statistician Karl Pearson plotted the heights of 10 randomly chosen sons versus that of their fathers.

The resulting data (in inches) were as follows.

A scatter diagram representing these data is presented in Figure 9.6.
Note that whereas the data appear to indicate that taller fathers tend to have taller sons, it also appears to indicate that the sons of fathers that are either extremely short or extremely tall tend to be more “average” than their fathers—that is, there is a “regression toward the mean.”
We will determine whether the preceding data are strong enough to prove that there is a regression toward the mean by taking this statement as the alternative hypothesis. That is, we will use the above data to test

Transcribed Image Text:

Fathers' height Sons' height 60 62 64 65 66 67 68 70 72 74 63.6 65.2 66 65.5 66.9 67.1 67.4 68.3 70.1 70