AP Statistics 2017

confirm by rejecting the null hypothesis. The alternative hypothesis is symbolized by H (^) A or H (^) a.
There are three possible forms for the alternative hypothesis: ≠, >, or <. If the null is H 0 : μ 1 – μ (^2)
= 0, then H (^) A could be:
H (^) A : μ 1 – μ 2 ≠ 0 (this is called a two-sided alternative )
or
H (^) A : μ 1 – μ 2 > 0 (this is a one-sided alternative )
or
H (^) A : μ 1 – μ 2 < 0 (also a one-sided alternative ).
(In the case of the one-sided alternative H (^) A : μ 1 – μ 2 > 0, the null hypothesis is sometimes written:
H 0 : μ 1 – μ 2 ≤ 0. This actually makes pretty good sense: if the researcher is wrong in a belief that
the difference is greater than 0, then any finding less than or equal to 0 fails to provide evidence in
favor of the alternative.)
• Identify which procedure you intend to use and show that the conditions for its use are present . We
identified the conditions for constructing a confidence interval in the first two sections of this chapter.
We will identify the conditions needed to do hypothesis testing in the following chapters. For the most
part, they are similar to those you have already studied.
If you are going to state a significance level α it can be done here.
• Compute the value of the test statistic and the P-value .
• Give a conclusion, linked to your computations, in the context of the problem .
Exam Tip: The four steps above have been incorporated into AP exam scoring for any question
involving a hypothesis test. Note that the third item (compute the value of the test statistic and the P -
value), the mechanics in the problem, is only one part of a complete solution. All four steps must be
present in order to receive a 4 (“complete response”) on the problem.
If you stated a significance level in the second step of the process, the conclusion can be based on a
comparison of the P -value with α. If you didn’t state a significance level, you can argue your conclusion
based on the value of the P -value alone: if it is small, you have evidence against the null; if it is not
small, you do not have evidence against the null.
Many statisticians will argue that you are better off to argue directly from the P -value and not use a
significance level. One reason for this is the arbitrariness of the P -value. That is, if α = 0.05, you would
reject the null hypothesis for a P -value of 0.04999 but not for a P -value of 0.05001 when, in reality,
there is no practical difference between them.
The conclusion can be (1) that we reject H 0 (because of a sufficiently small P -value) or (2) that we
do not reject H 0 (because the P -value is too large). We do NOT accept the null: we either reject it or
fail to reject it. If we reject H 0 , we can say in context that have convincing evidence in favor of H (^) A.
example: Consider, one last time, Todd and his claim that he can throw a ball 50 yards. His