Page 282 - ABCTE Study Guide_Neat

music. The whole point of inferential statistics is to help us infer characteristics of a population.

A sample is a subset of a population. Samples are useful when we want to draw conclusions about a
population, but it is impractical to collect information from the entire population. Perhaps it’s too costly to
do so or too time consuming, or maybe there are members of the population who are difficult to access for
any number of reasons. Ideally, the sample has everything in common with the population. Samples like
those are hard to create.

But there are some ways to create samples that are more reliable than others. A random sample is a
subset of a population in which every member of that population has the same chance of being chosen for
the sample.

How meaningful is it to you that four out of five dentists recommend using Supercalifragi-fluoride
toothpaste?

Are you suspicious? Why should you be? Maybe the sample included 1,000 doctors who were asked if
they would recommend the toothpaste. Maybe there were only five doctors in the sample. Would you be
more likely to buy the toothpaste if 95% of dentists surveyed use Supercalifragi-fluoride toothpaste in their
own homes?

Here’s the point: Random sampling is a great way to prevent bias. Nothing about the toothpaste
statements suggests any details of the study. For that reason, it’s reasonable to be suspicious.

Suppose you wanted to do a research project on liberal arts students’ attitudes toward statistics, you’re
likely to get a biased sample if you advertise the study in the school paper. Do you know why?

Students who take the time to respond to an ad and complete a survey are likely to have different
attitudes than those not taking the time to respond and complete the survey.

Just think about the attitudes of those who are willing to put comments in a suggestion box. Which do you
think the box would contain more of, complaints or compliments? Aren’t customer service departments
more often referred to as “complaint" departments than “compliment" departments?

Now suppose you’re doing a research project on the length of time students in all of the sections of a
particular statistics course spend studying for the next statistics test. You assign each student a number
and use a random number generator (like a computer program, for example). You get your random
sample, and it contains only women. Is your sample biased? See below to find out.

Is your sample bias?

The answer is no. Bias refers to the way the sample was formed, not the participants in the sample.
Fortunately, there’s something about randomness that makes this situation improbable. It has to do with
normal distributions. And normal distributions are related to probability. Even though your sample contains
only female students, your METHOD of sampling was random, so the sample itself is not biased. All that
said, when reporting the results of your study, you would still have to disclose that all participants were
women - simply by chance.

Question

In which of the following is random sampling most likely used?