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Chapter Six Notes Material Type: Notes; Professor: Pessoa; Class: STATISTICAL TECHNIQUES; Subject: Psychology; University: Indiana University - Bloomington; Term: Fall 2010;
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Probability allows us to establish a formal link between populations and samples. Helps answer the following question: Which samples can be (likely) obtained given a certain population. Inferential statistics utilizes this information to make inferences about populations from samples.
Relationship between samples and populations: What kinds of samples are likely?
What is the probability of selecting a king from a deck of cards? Can be restated as: What proportion of the whole deck consists of kings? In both cases, “4 out of 52”. p(king) = 4/ Probabilities can be expressed as fractions, decimals, or as percentages. 4/52 = .0769 = 7.69%
Probabilities range from 0 to 1. Probabilities must have positive values (or zero).
Diagram:
Properties:
The normal distribution is symmetrical. This means that the proportions on both sides of the mean are identical. All normal distributions have the same proportions.
Body height has a normal
= 6. If we select one person at random, what is the probability of selecting a person taller than 80? p (X > 80) =? z =
p(z > 2.0) =? p(X > 80) = p(z > +2.0) = 2.28%
Given the standard proportions of normal distributions we can give probabilities for z-scores with whole number values. But what about fractional z-scores? Need to use the unit normal table.
How the table is organized:
How do we use the unit normal table? Example: Find the proportion of the normal distribution corresponding to a z- score greater than z=+1.00. Draw a sketch … Then look up the value in the table.
For a normal distribution, what is the probability of selecting a z- score value greater than z=+1.0?
