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STAtistics / Mr. Hansen |
Name: ______________________ |
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1. |
Read recommendations 39 through 45 (pp. 26-27)
and the standards of evidence (pp. 110-113) from the recently released NMAP
report (National Mathematics Advisory Panel). For goodness’ sake, do not
print out the entire document. Simply read pages xxvi and xxvii that contain
the research recommendations, plus pages 82-85 (which are numbered 110-113 by
Adobe Acrobat). Then answer the following questions. |
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2. |
Translate the last sentence of the first
paragraph of recommendation 40 (i.e., the sentence that talks about adequate
statistical power) into layperson’s language. You may need to split this
sentence off into a small paragraph of its own to make it understandable. Do
not go into too much detail, and whatever you do, don’t use the term “Type II
error.” My reason for making this assignment is that I predict that some of
the readers of the report, even some who have math or math ed degrees, will not understand the sentence properly. |
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3. |
Do you agree or disagree with
recommendation 45? Write a short paragraph supporting your opinion. |
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4. |
From p. 82 (numbered 110 in Acrobat), we
know that the NMAP reviewed more than 16,000 (!) research studies but found
few of them worthy. How would the NMAP standards of evidence rate each of the
following? |
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(a) |
Two sections of STA sophomores, with 15+14
students, are taught traditional Algebra II by Mr. X. The other two sections,
with 13+18 students, are taught by Ms. Y using an experimental textbook. At
the end of the year, all four sections are given the same final exam. Scores
for Ms. Y’s students are found to be higher on average. There is no
attrition. Compute the one-tailed P-value
using your calculator, and determine the NMAP rating. Assume that neither class
exhibits pronounced skewness or outliers. |
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(b) |
Two sections of STA juniors, Mr. Z’s
students, are randomly assigned to receive instruction in logarithms (to
which they have had no prior exposure) by one of the following protocols:
either traditional instruction, in which they receive assignments from Mr. Z and
listen to his explanations in class, or modified instruction, in which they
receive the same assignments but are excused during class time to do whatever
they wish. At the end of the experiment, all students are given the same
exhaustive battery of standardized tests on logarithms, and their scores are
compared. There is no attrition. Compute the two-tailed P-value and determine the NMAP rating. Give specific rationales
for your decision. Assume that neither group exhibits pronounced skewness or outliers. |
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(c) |
Is the hypothetical study in part (a) a
controlled experiment? ________ |
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(d) |
Is the hypothetical study in part (b) a
controlled experiment? ________ |
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