5. Foundations for Inference

Question 1

What is point estimate?

Answer 1

Suppose a poll suggested the US President’s approval rating is 45%. We would consider 45% to
be a point estimate of the approval rating we might see if we collected responses from the entire
population. This entire-population response proportion is generally referred to as the parameter
of interest. When the parameter is a proportion, it is often denoted by p, and we often refer to the
sample proportion as ˆp (pronounced p-hat1
). Unless we collect responses from every individual in
the population, p remains unknown, and we use ˆp as our estimate of p.

Question 2

What is Sample error?

Answer 2

Sampling error, sometimes called sampling uncertainty, describes how much an estimate will
tend to vary from one sample to the next. For instance, the estimate from one sample might be 1%
too low while in another it may be 3% too high.

Question 3

What is bias?

Answer 3

Bias describes a systematic tendency to over- or under-estimate the true population value.
For example, if we were taking a student poll asking about support for a new college stadium, we’d
probably get a biased estimate of the stadium’s level of student support by wording the question as,
Do you support your school by supporting funding for the new stadium? We try to minimize bias
through thoughtful data collection procedures, which were discussed in Chapter 1 and are the topic
of many other books.