class-slides-02.pdf - Catolica-Lisbon School of Business...

Catolica-Lisbon School of Business and Economics
2 - Introduction to Sampling Distributions
Statistics II - Fall 2021
Filipa Reis
CLSBE
Statistics II 1/38

Agenda
1. Population, sample, and random sampling
2. Case Study: Defect Sampling
Statistics II 2/38

Population, Sample, and Random sampling
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Key concepts
•
A population is the complete set of all items (usually people, objects,
transactions, or events) that we are interested in studying.
•
A sample is a subset of units of a population.
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An experimental (or observational) unit is an object (e.g. person, thing,
transaction, event) about which we collect data.
•
A variable is a characteristic or property of an individual experimental (or
observational) unit in the population.
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Practice
Moodle Quiz (Lecture 2)
Q.1; Q.2; Q3
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Inferential statistics
How can we characterize a whole population using only a sample of data?
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A parameter is a numerical descriptive measure of a population. Because it
is based on the observations in the population, its value is almost always
unknown .
•
We use the information from a sample statistics to make inferences about
the parameters of a population .
•
A sample statistic is a numerical descriptive measure of a sample. It is
calculated from the observations in the sample.
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Population parameters and corresponding sample statistics
Population Parameter Sample Statistic
Mean μ ¯ x
Variance σ
2
s
2
Standard deviation
σ s
Binomial proportion
p ˆ p
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Probability distribution
A probability distribution is a table, graph, or mathematical function that
provides the probabilities of occurrence of the different possible outcomes
in an experiment .
1
•
Discrete Probability Distributions (probability mass functions, PMF)
•
Continuous Probability Distributions (probability density functions, PDF)
Features of probability distributions
We are usually interested in a few features of the distributions of random variables,
these include:
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Measures of central tendency
•
Measures of variability or spread
1
Visit to access an interactive website for creating and visualizing probability
distributions.
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Why sample?
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Thus far, we have assumed that we knew the probability distributions of the
random variables we were dealing with.
•
Using this knowledge, we computed means, variances, and probabilities.
•
However, in most practical applications, we don’t have this information; the
true ( population ) mean and standard deviation are unknown quantities that
have to be estimated .