Consider a professional basketball player.
Suppose he has two free throws.
Is the result of the second free throw independent of the first?
This has perplexed society for ages.
Our hypotheses are:
Complements of Kitchens (1998, Exploring Statistics, Pacific Grove, CA: Duxbury Press), we have data on two basketball players: Larry Bird and Rick Robey. Consider the data for Larry Bird (taken during the season 1980-1981).
test is extremely simple.
The above table are the observed frequencies.
Simply form the expected frequencies under H0
and obtain the
statistic discussed above, (1).
Our rejection rule changes slightly to:
How do we get the expected frequencies under H0?
Because , we fail to reject H0. It seems that Larry Bird's (at least in the season 1980-81) first and second freethrows were independent of one another.