III. Do the correct mechanics, including calculating the value of the test statistic and the P -value.
IV. State a correct conclusion in the context of the problem.Exam Tip: You are not required to number the four steps on the exam, but it is a good idea to do so—
then you are sure you have done everything required. Note that the correct mechanics are only worth
about 25% of the problem.z -Procedures versus t -Procedures
In this chapter, we explore inference for means and proportions. When we deal with means, we use t -
procedures, unless there is some unusual situation in which s is known. If that were to happen, use z -
procedures. With proportions, assuming the proper conditions are met, we deal only with large samples—
that is, with z -procedures.
When doing inference for a population mean, or for the difference between two population means, we
will usually use t -procedures. This is because z -procedures assume that we know the population
standard deviation (or deviations in the two-sample situation), which we rarely do. We typically use t -
procedures when doing inference for a population mean or for the difference between two population
means when:
(a) The sample is a simple random sample from the population
and
(b) The sample size is large (rule of thumb: n ≥ 30) or the population from which the sample is drawn is
approximately normally distributed (or, at least, does not depart dramatically from normal).
You could use z -procedures when doing inference for population means if:
(a) The samples are simple random samples from the population
and
(b) The population(s) from which the sample(s) is (are) drawn is normally distributed (in this case, the
sampling distribution of or x 1 – x 2 will also be normally distributed)
and
(c) The population standard deviation(s) is (are) known. This would be a rare situation and is unlikely
to be seen on the AP Exam.
Historically, many texts allowed you to use z procedures when doing inference for means if your
sample size was large enough to argue, based on the central limit theorem, that the sampling distribution
of or 1 – 2 is approximately normal. The basic assumption is that, for large samples, the sample
standard deviation s is a reasonable estimate of the population standard deviation σ . Today, most
statisticians would tell you that it’s better practice to always use t -procedures when doing inference for a
population mean or for the difference between two population means. You can receive credit on the AP
exam for doing a large sample problem for means using z -procedures if you specify that you are doing so
because the sample size is large, but it’s definitely better practice to use t -procedures.
When using t -procedures, it is important to check in step II of the hypothesis test procedure that the