|
Practical Statistics / Mr.
Hansen |
Name:
_____________________ |
Leap Day Test (100 pts.): Calculator Required
Write “OVER” if you need more
room. Keep your eyes on your own paper
at all times.
|
1. |
What is a statistic? ___________________________________________________ |
|
|
|
|
2. |
Give 5 examples of
statistics, 2 that measure central tendency, and 3 that measure spread: |
|
3. |
Recently, Mr. Hansen
assigned his STAtistics students to gather data on
the mean improvement in scores between Test 1 and Test 2, where Test 1
consisted of looking at the nonsense words |
|
|
|
|
(a) |
If D is the statistic of interest, is the mean of D positive, negative, or 0? Explain
briefly. |
|
|
|
|
|
|
|
|
|
|
|
|
|
(b) |
Estimate the standard
deviation of D and give a reason
for your answer. |
|
|
|
|
|
|
|
|
|
|
|
|
|
(c) |
Describe what shape you
would expect to see for the distribution of D. Explain briefly why this is your guess. |
|
(d) |
Is Mr. Hansen’s study an
experiment? Why or why not? |
|
|
|
|
|
|
|
|
|
|
|
|
|
(e) |
The STAtistics
students found strong evidence that Test 2 had a higher mean score. Does this
prove that the second test is easier? Why or why not? |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(f) |
What effect may well be
confounded with the differing difficulties of the two tests? |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(g) |
Suggest a redesign of the
experiment that would reduce the confounding factor in part (f). |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4.(a) |
Define Simpson’s Paradox. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(b) |
Give a sports-based example
of Simpson’s Paradox. Numbers are not required, but a sports context and a
description of why the result might seem “paradoxical” are required. |
|
|
|
|
|
|
|
(c) |
Luckily, Simpson’s Paradox is
not always a danger whenever 2 or
more snapshots of data are being examined in both an aggregated and a
disaggregated version. Explain, using words (required) and graphics
(optional), a situation in which Simpson’s Paradox simply cannot occur. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5.(a) |
Explain what is meant by “gerrymandering.”
There is a small bonus if you can also mention something about the origin of
the word. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(b) |
Can gerrymandering create an
example of Simpson’s Paradox? Why or why not? Be clear, and write several
good, solid sentences that demonstrate that you know what both terms mean in
relation to each other. |
|
6. |
True or false: All
experiments are controlled. ________ (If false, you must also mark up the
sentence to convert it into a true statement.) |
|
|
|
|
7. |
Does “randomization” in
experimental design refer to randomization of subject selection,
randomization of assignment, or both? Be sure to define what is meant by “randomization
of assignment.” |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
8.(a) |
Suppose I have a friend who
had a bad cold, but then he took some Zicam and
soon recovered. What kind of data do we have here? (Hint: It begins with the letter A.) |
|
|
|
|
|
__________________________
data |
|
|
|
|
(b) |
Suppose that I have 15
friends who are sniffling and sneezing, and after being given Zicam, 12 of them improve within a day. Is this an
experiment? Why or why not? |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(c) |
Describe what is meant by a
double-blind experiment. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(d) |
Design a double-blind
experiment that seeks to determine whether Zicam is
of any use in reducing the recovery time for cold sufferers. Be sure to
include an estimate of about how many test subjects you will need. Continue
on reverse side if necessary. |
|
(e) |
Imagine that 10 cold
sufferers treated with a placebo have a mean recovery time of 6.5 days, and
10 cold sufferers treated with Zicam have a mean
recovery time of 6.4 days. Is this result significant (meaningful) in the statistical sense? ____ In other
words, is this result something that cannot be plausibly explained by chance
alone? Explain why you think “yes” or “no.” |
|
(f) |
Would your answer to part
(e) change if you had a really large sample in which the mean recovery times
were 6.5 and 6.4? Why or why not? |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(g) |
Is the difference in part
(e) significant in a practical
sense (i.e., something that cold sufferers would care about)? Why or why not? |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(h) |
Is statistical significance
the same as practical significance? _______ |