Introduction
The emphasis in Chapters 2, 3 and 4 is on
descriptive statistics
. In those chapters we described
methods used to collect, organize, and present data, as well as measures of central location,
dispersion, and skewness used to summarize data. A second facet of statistics deals with
computing the chance that something will occur in the future. This facet of statistics is called
inferential statistics
.
An inference is a generalization about a population based on information obtained from a
sample. Probability plays a key role in inferential statistics. It is used to measure the
reasonableness that a particular sample could have come from a particular population.
What is Probability?
Probability
allows us to measure effectively the risks in selecting one alternative over the others.
In general, it is a number that describes the chance that something will happen.
Probability
: A value between zero and one, inclusive, describing the
relative possibility (chance or likelihood) an event will occur.
Probability
is expressed either as a percent or as a decimal. The likelihood that any particular
event will happen may assume values between 0 and 1.0. A value close to 0 indicates the event is
unlikely to occur, whereas a value close to 1.0 indicates that the event is quite likely to occur.
To illustrate, a value of 0.60 might express your degree of belief that tuition will be increased at
your college, and 0.50 the likelihood that your first marriage will end in divorce.
In our study of probability we will make extensive use of several key words. They are:
experiment, outcome
, and
event
.
Experiment
: A process that leads to the occurrence of one and only
one of several possible observations.
For example, you roll a die and observe the number of spots that appear face up. The experiment
is the act of rolling the die. Your survey company is hired by Ford to poll consumers to determine
if they plan to buy a new American made car this year. You contact a sample of 5,000 consumers.
The act of counting the consumers who indicated they would purchase an American made car is
the experiment.
Outcome
: A particular result of an experiment.
One outcome of the die rolling experiment is the appearance of a 6. In the experiment of
counting the number of consumers who plan to buy a new American-made car this year, one
possibility is that 2,258 plan to buy a car. Another outcome is that 142 plan to buy one.
Event
: A collection of one or more outcomes of an experiment.
Thus, the
event
that the number appearing face up in the die rolling experiment is an even
number is the collection of the
outcomes
2, 4, or 6. Similarly the event that more than half of
those surveyed plan to buy a new American made car is the collection of the outcomes 2,501,
2,502, 2,503, and so on all the way up to 5,000.
Approaches To Probability