2 of
10
1.2 Sampling populations
Government
consumer price index, trends in the economy, determine if there
is a recession, employment patterns, population trends, determine if you
should be audited, . . .
Politics
determine which political candidate is more popular, learn what con
stituents are mainly concerned about, . . .
Scientific research
clinical trials to investigate new drugs, estimation of fun
damental constants, psychological tests, . . .
Business
predict demand for a product, check quality of manufactured goods,
manage investment portfolios, calculate insurance rates, . . .
Quantum physics
quantum particles are fundamentally described by proba
bility.
Nearly every field uses statistics!
Outline of course
Six primary components of class
•
Fundamentals: what are statistics, parameters, experiments?
•
Descriptive statistics: how can we describe data?
•
Probability: what is the probability of . . .
•
Inferential statistics: inferences about populations from samples.
•
Hypothesis testing: using statistics to prove claims
•
Regression: modeling and prediction
1.2
Sampling populations
Example
1
.
The number of sexual partners an individual has provides useful
information to epidemiologists. An epidemiologist would like to estimate what
the mean (average) number of sexual partners is for US college students.
Question
1
.
What is the population we are interested in studying?
Question
2
.
How could we determine the true population mean?
Question
3
.
What are the drawbacks to a census?
Anthony Tanbakuchi
MAT167
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Statistics: The foundations
3 of
10
1.3
Basic definitions
Fundamental terminology
data
collected observations.
ex. number of sexual partners
h
=
{
3
,
2
,
4
,
0
,
6
,
2
,
8
,
7
,
3
,
11
, . . .
}
statistics methods
for planning experiments, obtaining data, and then or
ganizing, summarizing, presenting, analyzing, interpreting and making
conclusions based on the data.
population
the
complete
set of all data to be studied.
ex. US college students
census
collection of data from
every
member of the population.
sample
a
subcollection
of members selected from a population
ex. students at this institution are a
sample
of US college students
Two key statistical terms concerning data
parameter.
Definition 1.1
numerical measure describing a characteristic of a
population
.
ex. mean number of sexual partners for all US college students
statistic.
Definition 1.2
numerical measure describing a characteristic of a
sample
.
ex. mean mean number of sexual partners for a sample of students
from this institution.
The
parameter
is the
truth
we desire to find but doing a census is not
always possible or reasonable. Therefore, we use a
statistic
to
estimate
the
parameter.
Case Example II
Example
2
.
An epidemiologist would like to determine the mean (average)
number of sexual partners for our class. A census is not possible, so the epi
demiologist samples 10 students in the class.
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 Spring '11
 Tanbakuchi
 Statistics, sexual partners, Anthony Tanbakuchi

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