Suppose a well-known baseball player states that, at this stage of his career, he is a "300 hitter" or better. That is, he claims that he gets a hit in at least 30% of his at-bats. Over the next month of the baseball season, this player has 105 at-bats and gets 33 hits.
a. Identify the null and alternative hypotheses from the player's point of view.
b. Is there enough evidence from this month's data to reject the null hypothesis at the 5% significance level?
c. We might raise two issues with this test. First, does the data come from a random sample from some population? Second, what is the relevant population?
Discuss these issues. Do you think the test in part b is valid? Is it meaningful?