Transcript gis1e_alq_09_TP5

Active Learning Lecture Slides
For use with Classroom Response Systems
Introductory Statistics:
Exploring the World through Data, 1e
by Gould and Ryan
Chapter 9:
Inferring Population Means
© 2013 Pearson Education, Inc.
Slide 9 - 1
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The accuracy of an estimator is measured by
the standard error.
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Slide 9 - 2
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The precision of an estimator is measured by
the bias.
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Slide 9 - 3
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A sampling distribution is a probability
distribution of a statistic.
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Slide 9 - 4
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When a statistic of the sampling distribution is
the same value as the population parameter,
we say that the statistic is an unbiased
estimator.
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Slide 9 - 5
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The standard deviation of the sampling
distribution is what we call the standard error.
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Slide 9 - 6
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The standard error of the sample mean, gets
smaller with larger sample size.
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Slide 9 - 7
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For all populations, the sample mean is
unbiased when estimating the population
mean.
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Slide 9 - 8
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When considering the sampling distribution of
the sample mean, the larger the sample size, n,
the better the approximation. 50%
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Slide 9 - 9
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When considering the sampling distribution of
the sample mean, if the population is Normal to
begin with, then the sampling distribution is
exactly a Normal distribution.
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Slide 9 - 10
The sample mean is
A.
the arithmetic average of a
sample of data
B.
an estimate of a population
mean
C.
unbiased, if the sample is
a random sample
D.
all of the above
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Slide 9 - 11
The t-distributions are
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A.
symmetric
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unimodal
C.
“bell-shaped”
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all of the above
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Slide 9 - 12
Compared to the z-distribution, the
t-distribution has
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thinner tails
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thicker tails
C.
taller peaks
D.
more peaks
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The t-distribution’s shape depends
on only one parameter, called the
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A.
mean
B.
standard deviation
C.
degrees of freedom
D.
all of the above
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Slide 9 - 14
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Ultimately, when df is infinitely large, the
t-distribution is exactly the same as the
N(0, 1) distribution.
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Slide 9 - 15
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Confidence intervals are a technique for
communicating an estimate of the mean along
with a measure of our uncertainty in that
estimate.
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Slide 9 - 16
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A confidence interval can be interpreted as a
range of plausible values for the population
parameter.
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Slide 9 - 17
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The confidence level is a measure of how well
the method used to produce the confidence
interval performs.
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Slide 9 - 18
Which of the following are way(s) in which
we can report a confidence interval?
A.
(lower boundary, upper boundary)
B.
Estimate ± margin of error
C.
Mean ± standard deviation
D.
both A and B above
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Hypotheses are always statements about
population statistics.
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Slide 9 - 20
Which of the following value(s) for the
significance level α are good choice(s)?
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0.01
B.
0.05
C.
0.10
D.
all of the above
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Slide 9 - 21
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The t-statistic measures how far away (how
many standard errors) our observed mean, x ,
lies from the true population value μ.
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B.
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Slide 9 - 22
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In hypothesis testing, values of the
t-statistic that are far from 0 tend to discredit
the null hypothesis.
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The p-value tells us the probability that we
would get a t-statistic as extreme as or more
extreme than what we observed.
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There are three basic pairs of
hypotheses. The two-tailed one-sample ttest has the following hypotheses:
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H0: μ = μ0 and Ha: μ < μ0
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H0: μ = μ0 and Ha: μ ≠ μ0
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H0: μ = μ0 and Ha: μ > μ0
D.
H0: μ ≠ μ0 and Ha: μ = μ0
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© 2013 Pearson Education, Inc.
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Slide 9 - 25
There are three basic pairs of hypotheses.
The one-tailed (left) one-sample t-test has
the following hypotheses:
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H0: μ = μ0 and Ha: μ < μ0
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H0: μ = μ0 and Ha: μ ≠ μ0
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H0: μ = μ0 and Ha: μ > μ0
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H0: μ ≠ μ0 and Ha: μ = μ0
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Slide 9 - 26
There are three basic pairs of hypotheses. The
one-tailed (right) one-sample t-test has the
following hypotheses:
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H0: μ = μ0 and Ha: μ < μ0
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H0: μ = μ0 and Ha: μ ≠ μ0
C.
H0: μ = μ0 and Ha: μ > μ0
D.
H0: μ ≠ μ0 and Ha: μ = μ0
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© 2013 Pearson Education, Inc.
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Slide 9 - 27
When comparing two populations, if the data
sampled from the populations are one sample
of related pairs, then the samples are
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independent samples
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paired (dependent)
samples
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paired-independent
samples
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not random samples
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Slide 9 - 28
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With paired (dependent) samples, if you know
the value that a subject has in one group, then
you know something about the other group,
too.
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Slide 9 - 29
Which of the following are example(s) of
when dependence occurs?
A.
“before and after”
comparisons
B.
when the objects are related
somehow (comparing twins,
siblings, or spouses)
C.
when the experimenters have
deliberately matched
subjects in the groups to
have similar characteristics
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D.
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all of the above
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Slide 9 - 30
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With paired samples, we turn two samples into
one. We do this by finding the difference in
each pair.
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Slide 9 - 31