Transcript Review of Inference for Means

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I consistently calculate confidence intervals and test
statistics correctly, showing formula, substitutions,
correct critical values, and correct margins of error.
I consistently include all necessary steps in a
confidence interval or significance test, including a
check of conditions, hypotheses (for a test), and a
conclusion or interpretation in context.
I consistently and correctly explain what the
confidence interval or p-value means in the context
of the problem.
I consistently and correctly interpret the meaning of
95% confidence in the context of the problem.
I demonstrate an understanding that the
capture rate for a confidence interval is less
than advertised when the the population
standard deviation s is estimated by the
sample standard deviation s, unless
adjusted by using t instead of z.
 I demonstrate an understanding that the t
statistic is different from the z statistic, and
that this is due to using s to estimate s.
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I can explain how a difference in means
for two independent samples differs from
a matched pairs difference, both in the
design and in the interpretation of the
results.
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A simple random sample of 75 male
adults living in a particular suburb was
taken to study the amount of time they
spent per week doing rigorous exercise.
It indicated a mean of 73 minutes with a
standard deviation of 21 minutes. Find
the 95% confidence interval of the mean
for all males in the suburb. Interpret this
interval in words.
The gas mileage for a certain model of car
is known to have a standard deviation of 5
mi/gal. A simple random sample of 64 cars
of this model is chosen and found to have
a mean gas mileage of 27.5 mi/gal.
Construct a 95% confidence interval for
the mean gas mileage for this car. Interpret
the interval in words.
The president of an all-female school stated in an interview that she was
sure that students at her school studied more on average that the students
at a neighboring all-male school. The president of the all-male school
responded that he thought the mean student time for each student body
was undoubtedly the same and suggested that a study be taken to clear
up the controversy. Accordingly, independent samples were taken at the
two schools with the following results.
School
Sample Size Mean Study Standard
time (hrs)
Deviation
(hrs)
All Female
65
11.56
4.35
All Male
75
17.95
4.87
Determine at the 2% significance level if there is a significant difference
between the mean study times of the students in the two schools.
Six cars are selected randomly, equipped with one tire of
brand A and one tire of brand B (the other two tires are
not part of the test), and driven for a month. The amount
of wear (in thousandths of an inch) is listed in the table
below.
Car
1
2
3
4
5
6
Brand
A
125
64
94
38
90
106
Brand
B
133
65
103
37
102
115
At the = 0.05 level test the claim that the tire wear is the
same.
15/40 rule
 Ways to increase power?
 Comparison of t and z distributions
 When data isn’t normal
 When do you pool with means?
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Are they asking for a confidence interval or
significance test?
 Do I have one or two samples?
 Do I know anything about the population
SD?
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› If you do… well that’s z. If you don’t that’s t.
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If I have two samples are they
independent?
› If yes, mean1- mean 2.
› If no, look at the difference of means and go
back to “one sample” of all their differences