Transcript Chapter Nine - Bakersfield College

Chapter Nine
Using Probability to
Make Decisions about
Data
New Statistical Notation
• Odds are expressed as fractions or
ratios
• Chance is expressed as a percentage
• Probability is expressed as a decimal
• The symbol for probability is p
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Chapter 9 - 2
Probability
The probability of an event is equal to
the event’s relative frequency in the
population of possible events that can
occur.
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Chapter 9 - 3
Computing Probability
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Chapter 9 - 4
Probability Distributions
• A probability distribution indicates the
probability of all possible events in a
population
• An empirical probability distribution is created
by measuring the relative frequency of every
event in the population
• A theoretical probability distribution is a
theoretical model of the relative frequencies
of events in a population
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Chapter 9 - 5
Independent and
Dependent Events
• Two events are independent events
when the probability of one is not
influenced by the occurrence of the
other
• Two events are dependent events
when the probability of one is influenced
by the occurrence of the other
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Chapter 9 - 6
Sampling with and
without Replacement
• When sampling with replacement,
any previously selected individuals or
events are replaced back into the
population before drawing additional
ones
• When sampling without replacement,
previously selected individuals or events
are not replaced in the population
before selecting again
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Chapter 9 - 7
Obtaining Probability from the
Standard Normal Curve
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Chapter 9 - 8
Probability of Individual Scores
The proportion of the total area under the
normal curve for scores in any part of the
distribution equals the probability of those
scores.
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Chapter 9 - 9
Obtaining Probability
To compute probability, use the same
techniques you learned for finding the
area under the normal curve using z
scores and the z-tables.
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Chapter 9 - 10
Random Sampling and
Sampling Error
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Chapter 9 - 11
Representativeness
• Any sample may poorly represent one
population, or it may accurately
represent a different population
• The essence of inferential statistics is to
decide whether a sample of scores is
likely or unlikely to occur in a particular
population of scores
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Chapter 9 - 12
Representative Sample
• In a representative sample, the
characteristics of the individuals and
scores in the sample accurately reflect
the characteristics of individuals and
scores found in the population.
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Chapter 9 - 13
Sampling Error
• Sampling error occurs when random
chance produces a sample statistic that
is not equal to the population parameter
it represents.
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Chapter 9 - 14
Deciding Whether a Sample
Represents a Population
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Chapter 9 - 15
Region of Rejection
• At some point, a sample mean is so far above
or below the population mean that it is
unbelievable that chance produced such an
unrepresentative sample
• The areas beyond these points is called the
region of rejection
• The region of rejection is the part of a
sampling distribution containing values that
are so unlikely that we “reject” that they
represent the underlying raw score population
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Chapter 9 - 16
Means in the Region of Rejection Are So
Unrepresentative of This Population That It’s a
Better Bet They Represent Some Other Population.
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Chapter 9 - 17
Criterion
The criterion is the probability that
defines samples as too unlikely for us to
accept as representing a particular
population.
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Chapter 9 - 18
Rejection Rule
• When a sample’s z-score lies beyond
the critical value, reject that the sample
represents the underlying raw score
population reflected by the sampling
distribution
• When the z-score does not lie beyond
the critical value, retain the idea that the
sample may represent the underlying
raw score population
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Chapter 9 - 19