12.2 Tests about a Population Proportion (pp.766-777)
1. State the null hypothesis for a one proportion z-test.
2. State and use diagrams to illustrate the three possible alternative hypotheses for a one proportion
z-test.
3. Give the formula for the one-proportion z-statistic, and define each variable in the equation.
4. What assumptions must be met in order to use z procedures for inference about a proportion?
5. What additional information does a confidence interval provide that a significance test does not?
6. In which of the following situations can you safely use the methods of this section? Explain your
answers.
(a) You toss a coin 10 times in order to test the hypothesis 𝐻0 : 𝑝 = 0.5 that the coin is balanced.
(b) A college president says that “99% of the alumni support my firing of Coach Boggs.” You contact an
SRS of 200 of the college’s 15,000 alumni to test they hypothesis 𝐻0 : 𝑝 = 0.99.
(c) Do a majority of the 250 students in a statistics course agree that knowing statistics will help them in
their future careers? You interview an SRS of 20 students to test 𝐻0 : 𝑝 = 0.5.
7. In a recent year, 73% of first-year college students responding to a national survey identified “being
very well-off financially” as an important personal goal. A state university finds that 132 of an SRS of
200 of its first-year students say this goal is important.
(a) Is there good evidence that the proportion of all first-year students at this university who think being
very well-off is important differs from the national value, 73%? Carry out a significance test to help
answer this question.
(b) Construct and interpret a 95% confidence interval for the proportion of all first-year students at the
university who identify being well-off as an important personal goal. What additional information does
the confidence interval provide?
8. Any Miami Heat fan or archrival knows the team’s very large “SHAQilles heel” – the free-throw
shooting of the NBA’s most dominant center, Shaquille O’neal. Over his NBA career, Shaq made 53.3%
of his free throws.
Shaquille O’Neal worked in the off-season with an assistant coach on his free-throw technique. During
the first two games of the next season, Shaq made 26 out of 39 free throws.
(a) Do these results provide evidence that Shaq has significantly improved his free-throw shooting?
Justify your answer with appropriate evidence.
(b) Describe a Type I and a Type II error in this situation.