those getting above 80% are the same across the two populations.Free-Response
1.
I . Let p 1 = the true proportion of students who admit to using marijuana in 2004.
Let p 2 = the true proportion of students who admit to using marijuana in 2007.
H 0 : p 1 = p 2 (or H 0 : p 1 – p 2 = 0; or H 0 : p 1 ≤ p 2 ; or H 0 : p 1 – p 2 > 0).H (^) A : p 1 > p 2 (or H 0 : p 1 > p 2 ).
II . We will use a two-proportion z -test. The survey involved drawing random samples from
independent populations. , 100(0.27) = 27, 100(1 – 0.27) =
73, 175(0.171) ≈ 30, and 175(1 – 0.171) ≈ 145 are all greater than 10, so the conditions for
inference are present.
III .
(This problem can be done using 2-PropZTest in the STAT TESTS menu.)
IV . Since the P -value is quite small (a finding this extreme would occur only about 2.6% of the
time if there had been no decrease in usage), we have evidence that the rate of marijuana use
among students (at least among juniors and seniors) has decreased.
This is a paired study because the scores for each pair of twins are compared. Hence, it is a one-
sample situation, and there are 26 pieces of data to be analyzed, which are the 26 difference scores
between the twins. Hence, df = 26 – 1 = 25.
- • I is not correct. A confidence interval, at least in AP Statistics, cannot be used in any one-sided
hypothesis test—only two-sided tests.
• II is correct. A confidence interval constructed from a random sample that does not contain the
hypothesized value of the parameter can be considered statistically significant evidence against the
null hypothesis.
• III is not correct. The standard error for a confidence interval is based on the sample proportions is
The standard error for a significance test is based on the hypothesized population value is• IV is correct.
4.