A basketball player claims they are an 80% free throw shooter; that is, the player claims
that p = 0.80, where p is the true proportion of free throws the player
will make in the long run. We suspect the player is exaggerating and that p <
0.80.
Suppose the player shoots 50 free throws and makes 32 shots, a sample proportion of
p̂ = 32/50 = 0.64. This result gives some evidence that the player
makes less than 80% of free throws in the long run since 0.64 < 0.80. But does it give
convincing evidence that p < 0.80? Or, is it plausible (believable)
that an 80% shooter can have a performance this poor by chance alone? You can use a
simulation to find out.
For a more detailed discussion, see the description in The Practice of
Statistics, Statistics and Probability with Applications, or Introductory
Statistics: A Student-Centered Approach.
Investigate the possibilities yourself:
This free throw simulator assumes the player is truly an 80% free throw shooter.