NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M4
ALGEBRA II
Name
Date
1. Suppose you wanted to determine whether students who close their eyes are better able to estimate
when 30 sec. have passed than students who do not close their eyes. (You ask students to tell you when
to stop a stopwatch after they think 30 sec. have passed.) You find the first 50 students arriving at school
one day. For those 50, you flip a coin to decide whether or not they will close their eyes during the test.
Then you compare the amounts by which each group overestimated or underestimated.
a.
Did this study use random sampling? Explain your answer by describing what purpose random
sampling serves in such a study.
b.
Did this study make use of random assignment? Explain your answer by describing what purpose
random assignment serves in such a study.
c.
Would the study described above be an observational study or an experimental study? Explain how
you are deciding.
2. A Gallup poll conducted July 10–14, 2013 asked a random sample of U.S. adults: “How much attention do
you pay to the nutritional information that is printed on restaurant menus or posted in restaurants,
including calories and sugar and fat content.” The sample results were that 43% of the respondents said
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M4
ALGEBRA II
they pay a “fair amount” or a “great deal” of attention. Suppose there had been 500 people in the study.
The following graph displays the results from 1,000 random samples (each with sample size 500) from a
very large population where 50% of respondents “pay some attention" and 50% “pay little or no
attention.”
 sample proportion 
a.
Based on the simulation results above, are the sample data (43% responding “pay some attention”)
consistent with the simulation? In other words, do these results cause you to question whether the
population is 50/50 on this issue? Explain.
b.
Do you believe it is reasonable to generalize the results from this study to all U.S. adults? Explain.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M4
ALGEBRA II
Assessment Task Item
Highly Effective:
Effective:
Developing:
Ineffective:
Gives a correct answer
Gives a correct answer with
Incorrect or
Incorrect of
with substantial
some evidence of
missing answer
missing answer
evidence of
mathematical reasoning to
but shows
with little to no
mathematical
solve a problem
evidence of some
evidence of
reasoning and
OR
mathematical
mathematical
implementation to
Gives an incorrect answer
reasoning and
reasoning and
solve a problem.
with substantial evidence
implementation of
implementation
of mathematical reasoning
mathematics to
of mathematics
and implementation to
solve the problem
to solve the
solve a problem
problem
Correctly states the
Says the study did not use
Confuses random
Provides an
study did not use
random sampling
sampling with other
answer that is not
random sampling
BUT
various random
relevant to the
AND
Describes the purpose of
forms like random
statistical study
Describes the purpose
random sampling incorrectly
assignment.
given.
statistical studies
as attaining a
(ex- to draw cause-and-
and explains how
representative sample.
effect-conclusions)
Correctly says the study
Says the study did use
Confuses random
Provides an
did use random
random assignment
assignment with
answer that is not
assignment
BUT
other various
relevant to the
AND
Describes the purpose of
random forms like
statistical study
Describes the purpose
random assignment
random sampling.
given.
in terms of balancing
incorrectly (ex-only to draw
out confounding
cause-and-effect-conclusions
variables.
but with no explanation why
a.
1. Recognize the
purpose and
S-IC.B.3
differences among
randomization
b.
relates to each.
S-IC.B.3
that works)
c.
S-IC.B.3
Identifies the study as
Identifies the study as
Identifies the study
Answer shows
experimental
experimental
as observational
inconsistency with
AND
BUT
AND/OR
a choice between
The justification is
The reasoning is inconsistent
The reasoning is
the two types of
correct.
with the student’s choice.
inconsistent with
studies.
the student’s
choice.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M4
ALGEBRA II
2. Making
a.
Uses the observed
Makes an attempt to
Replies “no”
Student does not
statistic (0.43) and the
integrate information from
because the center
refer to the
simulated distribution
the observed statistic and
of the simulated
simulated
graph to address the
the simulated distribution
distribution is close
distribution in
parameter based
question of whether the
but the response is
to .50.
their response.
on a random
population is 50/50 (ex-
inconsistent (ex- “.43 is on
sample
“Yes, because 0.43 is far
the graph so I believe the
in the tail of this
population is 50/50)
distribution”).
OR
Statistical Inference
about a
S-IC.A.2
populations
Makes a conclusion that
cannot be inferred (ex- We
have proven that the
population is 50/50)
b.
S-IC.A.1
Indicates the Gallup Poll
Attempts to use random
Replies “no” and
Does not justify
uses a random sample
sampling in order to justify
claims the sample is
their answer.
of U.S. adults to argue
reasoning but is to with the
too small
that it would be suitable
43% being too different
OR
to generalize the results
from 50%.
Says only adults
to the larger population
were surveyed
of U.S. adults.
OR
Claims that
representing an
entire population is
impossible