a grudge is a heavy thing to carry.. probability the probability of an event is the proportion of...
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A grudge is a heavy
thing to carry.
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Probability
The probability of an event is the proportion of times we would expect the event to occur in an infinitely long
series of identical sampling experiments.
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Probability
If all the possible outcomes are equally likely, the
probability of the occurrence of an event is equal to the proportion of the possible outcomes characterized by
the event.
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Probability
Probability is a very useful notion in situations involving
at least some degree of uncertainty; it gives us a way of expressing the degree of assurance that a particular
event will occur.
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Probability
Chance factors inherent in forming samples always affect sample results. Sample results must therefore be interpreted
with that in mind.
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Probability
The probability of occurrence of either one event OR another
OR… is obtained by adding their individual probabilities, provided
the events are mutually exclusive.
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Probability
The probability of the joint occurrence of one event AND
another AND another AND another… is obtained by
multiplying their separate probabilities, provided the events are independent.
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Probability
Any relative frequency distribution may be interpreted
as a probability distribution.
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Probability
Pr = .15 + .30 + .40 = .85 (85% chance)
Grade Relative Frequency
A .15
B .30
C .40
D .10
F .05
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Your CCHHAANNCCEEFor a break coming up soon!
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Confidence Statement
Statistic ± Margin of Error
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Margin of Error
1
n
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Confidence Interval
A range of values constructed from sample data so the
parameter occurs within that range at a specified
probability. The specified level of probability is called
the level of confidence.
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Confidence Interval for a Sample Mean
X + Z((
SN
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We’re We’re CONFIDENTCONFIDENT
there’s a there’s a P P R R O O B B A A B B I I L L I I T T YY
you want a breakyou want a break
Stand up and take
a short break
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Confidence Interval
95% of those surveyed will fall
into a certain range surrounding the mean
95% Confidence Interval
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Confidence Interval
The average size of a mortgage applied for in 1993 was $116,991 as
opposed to $119,999 in 1992. A sample of 64 mortgages showed that the standard deviation of the amount applied for was $6019. Find a 95% confidence interval for the average
size of a mortgage applied for in 1993.
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Z = 1.96
Confidence Interval
s = 6019
C =95%i
n = 64
x = $116,991
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Confidence Interval
X ± Z( s / √n) = 116,991 ± 1.96( 6019 / √64 ) =
116,991 ± 1.96(752.38) =116,991 ± 1474.66 =
115516.34 to
118465.66
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Confidence Interval
According to the Family Economic Research Group of the US Department of Agriculture, middle income couples who had babies in 1992 will spend an average of $128,670 by the time the baby is 18 years old. Assume the standard deviation of a sample of 100
families was $8473. Find a 90% confidence interval for the average
cost to raise a child born in 1992.
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Z = 1.645
n = 100s = 8473
X = 128,670C = 90%
i
Confidence Interval
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Confidence Interval
X ± Z( s / √n) =
128,670 ± 1.645( 8473 / √100) =
128,670 ± 1.645(847.3) =
128670 ± 1393.81 =
127276.19
to
130063.81
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Confidence Interval for Confidence Interval for aa Sample Proportion Sample Proportion
p + Z p(1 - p(
n
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Confidence Interval for a Sample Proportion
Suppose 1,600 of 2000 union members sampled said they plan to vote for the
proposal to merge with the UMA. Using the .95 level of confidence, what is the
interval estimate for the population proportion? Based on the
confidence interval,what conclusion can be drawn?
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p + Z p (1 - p
(n
=.80 + 1.96.80(1-.80)
2,000
= .80 + 1.96 .00008
= .782 and .818
Confidence Interval for a Sample Proportion
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Point Estimate
A value, computed from sample information that is used to
estimate the population parameter
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Standard Error of the Sample Mean
The standard deviation of the sampling distribution of the
sample means. It is a measure of the variability of the sampling distribution of
the sample mean.
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Look at the explanation provided in your textbook
Pages 429-434
Central Limit Theorem
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REMINDER:REMINDER:
Chapter 18 will be an important reference
for this section of statistics
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Experimental Process
Subjects
Treatment
Observation
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VariablesExplanatory Variable
(Independent variable)
Response Variable(Dependent variable)
Lurking of Confounding Variable
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Alternative Experimental Designs
Completely Randomized Design
Block Design
Matched Pairs Design
Double Blind Design
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Completely Randomized Design
Simplest Design Strategy
Each subject is randomly assigned to one group
Typically, group sizes are
identical
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Completely Randomized Design SubjectsSubjects Group AGroup A Group BGroup B Group CGroup C
AdamsAdams XX
AllenAllen XX
BaileyBailey XX
DaltonDalton XX
GrayGray XX
JamesJames XX
RobertsRoberts XX
SmithSmith XX
WhiteWhite XX
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Block DesignUsed when known extraneous variables
may influence the experiment
Subjects are pre-sorted by the influencing variables, then partitioned into similar
blocks
Subjects from each block are randomly
assigned to groups
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One-Dimensional Block Design
to Control AgeAge Subject Group A Group B Group C
16 Gray
17 May May Gray Lee
20 Lee
28 Jones
29 Cooper Smith Jones Cooper
29 Smith
30 Adams
33 Brown Brown Adams Magee
34 Magee
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Matched Pairs Design
Each subject receives each treatment
Treatment sequence is randomly chosen for each
subject
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Matched Pairs Design
Subjects Treatment Order
Adams A B C
Allen A C B
Bailey B A C
Dalton C B A
Gray A B C
James C B A
Roberts B C A
Smith C A B
White A C B
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Double Blind Experiment
Neither the subjects nor the investigators know which treatment is administered
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Control
Minimize the effects of lurking/confounding variables on the response, most simply
by comparing several treatments.
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Randomize
Use impersonal chance to assign subjects to treatments.
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Replicate
Repeat the experiment on many subjects to reduce chance
variation in the results.
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Statistical Significance
An observed effect so large that it would rarely occur by chance.