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.

Results so far:

Activity complete!

In the simulation, the player made of 50 shots (p̂ = ).