Question

Suppose that a basketball player (let’s call her Tamika) has had a .6 probability of successfully

making a foul shot (trial) during her career. Suppose further that Tamika wants to convince the

coach that she has improved to the extent that her probability of success is now .8 rather than .6.

The coach agrees to allow Tamika to take 10 shots in an effort to convince him that she has

improved to this extent. Let the random variable X represent the number of shots that Tamika

makes successfully, and let p represent Tamika’s actual probability of success. If p = .6, then

Tamika has not improved. If p = .8, then Tamika has improved to the extent she claimed. Throughout this assignment we will assume that Tamika’s shots constitute a random

sample of independent trials with a constant probability of success.

a) Suppose that Tamika has not improved. Identify the probability distribution of X (its name

and also its parameter values.)

Suppose for now that the coach uses the following decision rule: he will only be convinced that

Tamika has improved if she makes all 10 shots successfully.

b) Report the probability that Tamika will successfully make all 10 shots, if she really has not

improved. (Show how you calculate this.) Would you say that it’s very unlikely that she’ll

convince the coach that she has improved, if she really has not improved? (This is called a Type

I error.)

c) Now suppose that Tamika has improved to the extent she claimed. Determine the probability

that she will successfully make fewer than 10 shots. (Show how you calculate this.) Would you

say that it’s very unlikely that she’ll fail to convince the coach that she has improved, if she

really has improved? (This is called a Type II error.)

Answer 1