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STAtistics / Mr. Hansen |
Name: _______________________________________ |
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9/16/2008 |
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Test #1 (100 points): Calculator permitted throughout
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1.(a) |
(4 pts.) What is a
statistic? ___________________________________________ |
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(b) |
(3 pts.) Give several
examples of statistics. _________________________________ |
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_____________________________________________________________ |
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2. |
(4 pts.) What is a parameter?
_____________________________________________ |
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3. |
(3 pts.) The second half of
our course, known as “inferential statistics,” can be summarized by the
following sentence that uses some words from #1 and #2: |
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________________________________________________________________ |
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4. |
(2 pts.) The first half of
our course, from now until midterm exams, is concerned with exploratory data analysis, experimental
design, and probability. When we
run our group surveys this week and next, which of these three topic areas
will we be exploring? _________________________________ Hint: An experiment is a special type of study in which we impose
some type of treatment—beyond mere data gathering—on our test subjects. As
you know, a good experiment should always also have a control group that
receives no treatment or only a dummy (placebo) treatment. |
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5. |
(28 pts.) Carefully draw
lines to match each letter with its official name and its description. |
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Letter |
Official Name |
Description |
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s |
sample standard deviation |
total of sampled data
values, divided by n |
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linear correlation
coefficient |
mean squared deviation from
the population mean |
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n |
sample size |
square root of sample
variance |
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population standard
deviation |
square root of population
variance |
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population variance |
number of data points in
the sample |
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population mean |
number between –1 and +1
that indicates strength and direction of linear fit in a scatterplot |
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r |
sample mean |
equals population median
for a symmetric distribution |
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6. |
(6 pts.) Fill in the
blanks: IQR, which stands for __________________________ ,
is a ____________ measure of dispersion, which means that it is not affected by
outliers. However, s.d., which stands for
_____________ _____________ , is strongly
affected by outliers. |
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7. |
(6 pts.) Describe how you
would determine whether a certain data value, say, x, is an outlier in a data set. Be sure to use the terms Q1 and Q3 in your description. You do not need to define what
they mean. |
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8. |
(4 pts.) What is the
percentile for the Q3
value in a data set? ______ What is the z
score (approximately) that corresponds to this percentile? _______ (No work
is expected for either answer.) |
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9. |
(6 pts.) Briefly state the
distinction between a scientific theory
and an unscientific theory. An
explanation is not required. |
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10. |
(3 pts.) What number or value
tells us how many standard deviations a point lies to the left or right of
the mean? _________ |
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11. |
Guinea pig lifespans are skew right. Make a sketch of a phony histogram
and a phony normal quantile plot to illustrate this right skewness. Label
your axes (name, numbers, and units if applicable) in the histogram but not
in the NQP. MAKE UP THE NUMBERS. DO
NOT USE YOUR CALCULATOR. |
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(a) |
(4 pts.) Histogram: |
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(b) |
(4 pts.) NQP: |
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(c) |
(6 pts.) The 5-number
summary for human lifespans in the Republic of Oxonia is 0, 63, 77, 84, 108. Is
the distribution skew left, skew right, or symmetric? _______________ Sketch
a regular boxplot, making a reasonable effort to
show scaling correctly. (In other words, do not randomly slap down a box in
which the distance from 63 to 77 looks the same as the distance from 77 to
84.) |
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12. |
In the 2004 Presidential
election, exit pollsters incorrectly predicted that Kerry would win in Ohio,
based on their interviews with (mostly) randomly chosen voters who were, in
some cases, asked to wait in line for a while because of the heavy voter
turnout. Pollsters exercised some personal discretion in their choice of
polling subjects during periods when multiple voters were leaving
simultaneously and when there was ambiguity in the results of the random
number generation. Pollsters employed on election day were primarily
college-aged people looking for extra income. |
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(a) |
(6 pts.) Explain briefly
what was wrong with the methodology and why it led to erroneous results. |
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(b) |
(6 pts.) If the pollsters’
ages (in years) were normally distributed with mean 20 and standard deviation
2, compute the following. |
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Percentage of pollsters who
were less than 21 years old = ____________ |
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13. |
(7 pts.) (Work is optional for this problem.
However, there is no partial credit unless you show your work. Use the blank region
if you wish to show your work.) Mr. Hansen’s uncle, a German teacher, is
known as an easy grader. If student test scores are normally distributed in
Mr. Hansen’s uncle’s classes, with mean 88 and standard deviation 8, find the
score to the nearest tenth needed
to be at . . . |
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