Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 7.5 | Looking Ahead to Inferential Statistics 215
3. For a particular population, the standard distance between a sample mean and the
population mean is 5 points for samples of n = 4 scores. What would the standard
distance be for samples of n = 16 scores?
a. 5 points
b. 4 points
c. 2.5 points
d. 1 point
ANSWERS
1. C, 2. D, 3. C
7.5 Looking Ahead to Inferential Statistics
LEARNING OBJECTIVE
7. Explain how the distribution of sample means can be used to evaluate a treatment
effect by identifying likely and very unlikely samples.
Inferential statistics are methods that use sample data as the basis for drawing general
conclusions about populations. However, we have noted that a sample is not expected to
give a perfectly accurate reflection of its population. In particular, there will be some error
or discrepancy between a sample statistic and the corresponding population parameter.
In this chapter, we focused on sample means and observed that a sample mean will not
be exactly equal to the population mean. The standard error of M specifies how much
difference is expected on average between the mean for a sample and the mean for the
population.
The natural differences that exist between samples and populations introduce a degree
of uncertainty and error into all inferential processes. Specifically, there is always a margin
of error that must be considered whenever a researcher uses a sample mean as the basis
for drawing a conclusion about a population mean. Remember that the sample mean is not
perfect. In the next seven chapters we introduce a variety of statistical methods that all use
sample means to draw inferences about population means.
In each case, the distribution of sample means and the standard error will be critical elements
in the inferential process. Before we begin this series of chapters, we pause briefly
to demonstrate how the distribution of sample means, along with z-scores and probability,
can help us use sample means to draw inferences about population means.
EXAMPLE 7.7
Suppose that a psychologist is planning a research study to evaluate the effect of a new
growth hormone. It is known that regular, adult rats (with no hormone) weigh an average
of μ = 400 g. Of course, not all rats are the same size, and the distribution of their weights
is normal with σ = 20. The psychologist plans to select a sample of n = 25 newborn rats,
inject them with the hormone, and then measure their weights when they become adults.
The structure of this research study is shown in Figure 7.11.
The psychologist will make a decision about the effect of the hormone by comparing
the sample of treated rats with the regular untreated rats in the original population.
If the treated rats in the sample are noticeably different from untreated rats, then
the researcher has evidence that the hormone has an effect. The problem is to determine
exactly how much difference is necessary before we can say that the sample is
noticeably different.