The tosses of the coin can be treated as a random sample of coin tosses. Both n and n (1 – )
are greater than or equal to 10 (or 5). And we have true independence because we are not
sampling without replacement from a finite population, we can construct a 99% z interval for
the population proportion:We are 99% confident that the true proportion of heads for this coin is between 0.484 and 0.69.
If the coin were fair, we would expect, on average, 50% heads. Since 0.50 is in the interval, it
is a plausible population value for this coin. We do not have convincing evidence that Brittany’s
coin is bad.
Generally, you should use t procedures for one- or two-sample problems (those that involve means)
unless you are given the population standard deviation(s) and z -procedures for one- or two-
proportion problems.Calculator Tip: The STAT TESTS menu on your TI-83/84 contains all of the confi-dence intervals you
will encounter in this course: ZInterval (rarely used unless you know σ); TInterval (for a
population mean, “one-sample”); 2-SampZInt (rarely used unless you know both σ 1 and σ 2 ); 2-
SampTInt (for the difference between two population means); 1-PropZInt (for a single population
proportion); 2-PropZInt (for the dif-ference between two population proportions); and LinRegTInt
(see Chapter 13 , newer TI-84s only). All except the last of these are covered in this chapter.Exam Tip: There are three steps to a confidence interval: Check conditions and identify the procedure,
compute the interval, interpret the interval in context. The question may not specifically ask for all three
steps, but they are always required unless specifically stated otherwise.
example: The following data were collected as part of a study. Construct a 90% confidence
interval for the true difference between the means (μ 1 – μ 2 ). Does it seem likely the
difference in the sample means indicates that there is a difference between the population
means? The samples were SRSs from independent, approximately normal populations.