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ATHK1001 Assignment
Creation date：2024-05-22 14:27:07
Belonging category：数学mathematics
Assignment

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ATHK1001 Assignment 1

Assignment 
Late penalties of 5% per day apply.
• Online submission: All submissions are to be
made online via the ATHK1001 Canvas website.
Submissions will be checked for plagiarism. You
may not use AI tools to assist you.
• Word length: 750 words across all questions
(except references in Question 13). Penalties will
apply to papers that exceed this limit by more
than 10%.
• Total marks: 60 (15% of total grade for class)
Background to Assignment 1
• A useful skill when dealing with data is being able
to estimate plausible answers to questions you
don’t know the answer to.
• A strategy for doing this is embodied by what are
known as “Fermi problems.”
– A common example is “How many piano tuners are
there in Chicago?”
– Most people have no idea, but perhaps they can
answer if we turn it into a Fermi problem.
Fermi problems
• Could breakdown “How many piano tuners are there in
Chicago?” into a series of sub-question you may be
better at estimating:
– How many people are there in Chicago? How many
families? What proportion of families have a piano?
How often does a piano have to be tuned? How long
does it take to tune a piano? How many days a year
would a piano tuner work?
• Ärlebäck & Albarracín (2019) reviewed evidence that
Fermi problems are used in science education, but
found no studies testing if they led to better estimates.
• We tested this in the experiment you did in Week 2.
Our experiment
• You answered nine question setup as Fermi problems
(i.e., with sub-questions) and nine as Non-Fermi
problems.
• Two sets of questions were used each with a Fermi
problem version (i.e., target question with sub-
questions) and a Non-Fermi version (i.e., target
question with no sub-questions).
– A “multiplicative” set of questions in which multiplying the
sub-questions helps answer the target question (e.g.,
“How many piano tuners are there in Chicago?”)
– An “additive” set of questions in which adding the sub-
questions helps answer the target question (e.g., “What is
the total military budgets of the members of the UN
Security council (USA, Russia, China, UK, France), in
millions of $US?”)
Two groups
• Participants were randomly assigned to one of two
conditions:
– The “Multiplicative condition” in which participants’ Fermi
problems came from the multiplicative set of questions,
and their Non-Fermi problems came from the additive set
of questions.
– The “Additive condition” in which participants’ Fermi
problems came from the additive set of questions, and
their Non-Fermi problems came from the multiplicative set
of questions.
• So everyone answered both sets questions, had both Fermi
and Non-Fermi problems, and the control group for each
condition came from the other condition.
• We also randomly varied the order of questions, but we did
not analyse the effects of order.
What a trial looked like
Hypotheses
• Hypothesis 1: Mean accuracy for Fermi problems will be
different than for Non-Fermi problems. We predict accuracy will
be greater for Fermi problems.
• Hypothesis 2: Mean accuracy for Fermi problems will not differ
between “Multiplicative condition” and the “Additive
condition”.
• Hypothesis 3: Mean accuracy for Non-Fermi problems will not
be differ between “Multiplicative condition” and the “Additive
condition”.
• Hypothesis 4: Accuracy for Fermi problems will correlate with
accuracy for Non-Fermi problems.
• How we test such hypotheses will be covered in lectures in
Week 4 and 5, and in Week 5 tutorials.
Participants
• A number of students who did the experiment
are not part of the data set.
– Some students did not have their data
correctly recorded.
– Some students did not complete enough of
the experiment.
– Some students did not consent to having
their data included.
• This left a data set of 197 ATHK1001 students.
Results
• Data file “Assignment1_dataset.xls” has been put on our
Canvas website. Each line represents a participant.
• First column “id number” is an arbitrary ID number
generated by the computer.
• The second “condition” column represent an
independent variable
– 1 indicates “Multiplicative condition”
– 2 indicate “Additive condition”.
• The column “Accuracy for Fermi problems” is the
participant’s accuracy on their Fermi problem questions.
• The column “Accuracy for Non-Fermi problems” is the
participant’s accuracy on their Non-Fermi problem
questions.
How is accuracy calculated
• How the two dependant variables are calculated is critical.
• We do not expect Fermi problems to lead people to estimate the
exact right answer, often the goal is just to estimate the answer to
the right order of magnitude (power of 10).
– E.g., any answer between 100 and 999 has an order of magnitude of 2.
• For each students’ set of Fermi problems how many answer had
the right order of magnitude was counted and divided by the
number of Fermi problems they answered.
– This is “Accuracy for Fermi problems” and is a proportion between 0.0 and
1.0.
• For each students’ set of Non-Fermi problems how many answer
had the right order of magnitude was counted and divided by the
number of Non-Fermi problems they answered.
– This is “Accuracy for Non-Fermi problems” and is a proportion between 0.0
and 1.0.
Your task
• Use Excel (or similar program) to analyse this data and
determine if the hypotheses have been supported.
• There are 13 questions to answer, each worth a
specified number of marks.
• Answer these questions with complete sentences
(except where a graph is requested), but do not repeat
the questions themselves. Don’t use tables.
• Some questions ask you to give interpretations, just try
to use your judgement and the tools you have been
given in the course to answer as well as you can.
– There are not necessarily single correct answers to such
questions.
Readings
• You should read at Ärlebäck and Albarracín (2019) so
as to understand what Fermi problems are and how
they have been used.
– This article can be found in the library but will be available
on the “Reading list” accessible from ATHK1001’s Canvas
page.
• You do not need to read anything else on this topic in
order to be able to write an excellent assignment.
– You can read more widely if you wish. However, if you use
words or ideas from something you read then you must
properly cite it.
Formatting recommendations
• Our preference is that you use the font “Times
New Roman”, 12-point size, and double-space
all the lines.
– Indent the beginning of each paragraph using one
tab space.
• You should use APA style referencing and
citations, but we will accept other styles.
Case category
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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