Download I can do 3.1-3.7

Achievement Standard Statistics and Modelling 3.1
Achievement:
Determine the trend for time series data
3 Credits
Internal
I can
Nulake Sigma
graph time series.
2 - 44
Ch 13
smooth a time series with moving averages.
20-28
Ch 13
describe the trend in context using smoothed data.
29-33
Ch 13
calculate and/or estimate seasonal effects.
34-44
Ch 13
make forecasts based on a trend line fitted to smoothed data with seasonal effects.
34-44
Ch 13
Merit:
I can
I can
analyse a time series based on data that cannot be modelled by a single straight linear
trend over its entire range.
choose and justify a model for the analysis of a time series
Excellence
seasonally adjust data and interpret the results in context
compare two sets of related time series data
use formal methods of analysis (eg least squares regression lines).
report on the relevance and usefulness of forecast
discuss the features of the time series data
report on potential sources of bias
suggest improvements to the model used for the analysis of a time series
comment on limitations of the analysis of a time series
Time series data may be represented by an index series.
Use of appropriate technology is expected.
Achievement Standard Statistics and Modelling 3.2
Merit:
Achievement:
Calculate confidence intervals for population parameters
3 Credits
I can
Nulake
Sigma
calculate large sample confidence intervals for the mean of a population
80-83
Ex14.1
calculate large sample confidence intervals for the proportion of a population
84-87
Ex14.3
I can
Nulake
Sigma
interpret confidence intervals
97-101
calculate the sample size required to meet a pre-specified precision
92-96
Ex14.2
Ex14.4
perform calculations involving the difference between two population means
88-91
Ex14.5
Nulake
Sigma
I can
Excellence
External
describe the applications of the Central Limit Theorem
73-77
Ex11.111.5
calculate the standard error of an estimate
73-77
181
analyse the estimates of population parameters (eg discuss the precision).
73-77
use sigma notation in a proof
Use of appropriate technology is expected.
276
Achievement Standard Statistics and Modelling 3.3
Solve straightforward problems involving probability
4
Credits
I can
calculate probabilities involving mutually exclusive events
calculate probabilities involving independent events
Achievement:
calculate probabilities involving complementary events
External
Nulake
Sigma
P108111,170
P108111,p170
Merit:
Ex 1.3
P125-130
Ex1.3
calculate expected values or variance of random variables from a given discrete
probability distribution.
P146-159
Ex
1.1,2.22.10
calculate probabilities using theoretical and experimental probability
P108-111
1
calculate probabilities using use tree diagrams
P112-116
calculate probabilities using Venn diagrams
P123-130
Ex 1.2
calculate probabilities using permutations and combinations
P131-146
Ex 3.13.5
calculate probabilities involving combined events.
use basic sigma notation
Excellence
Ex 1.3
Ex 1.4
P276
I can
Nulake
Sigma
solve problems from those situations listed for achievement.
P164-170
Ex 1.6
solve problems involving conditional probability
P116-122
Ex
1.5,1.6
I can
Nulake
Sigma
apply probability theory using combinations of techniques
P164-170
apply probability theory using non-numeric reasoning
P164-170
prove selected probability theories
P164-170
use sigma notation if required in calculations or proofs.
Use of appropriate technology is expected.
Achievement Standard Statistics and Modelling 3.4
Solve equations
4 Credits
Achievement:
I can
Sigma
172-178
182-187
Ex21.1,
21.2
solve a non-linear equation using the Newton-Raphson method with a given
starting value (only derivatives of polynomials are required)
193-199
Ex23.4
solve a non-linear equation using the bisection method with a given starting
interval
188-191
Ex23.3
optimise an objective function for a situation requiring techniques of linear
programming, where the constraints and the objective function for the problem
are given.
200-210
Ex22.4,
22.5
I can
Nulake
Sigma
form and solve a system of linear equations.
182, 187
211-215
220-223
211-215
220-223
Ex21.2
-21.4
Ex22.3
22.5
Ex22.4
-22.5
find appropriate solutions to a non-linear equation using the Newton-Raphson
method to improve the approximation to a stated precision or for a specified
number of iterations.
216-219
Ex23.4
find appropriate solutions to a non-linear equation using the bisection method to
improve the approximation to a stated precision or for a specified number of
iterations.
216-217
Ex23.3
I can
Nulake
interpret the consistency or non–independence of systems of equations,
179-181
optimise an objective function for the linear programming problem.
Merit:
Nulake
solve systems of three linear equations in three variables, where there is a
unique solution
form constraints and the objective function for a linear programming problem.
consider sensible rounding of an answer to an linear programming problem
use a graph, table or graphics calculator to find an approximate solution to a nonlinear equation
represent geometrically non–independent systems of equations,
Excellence
External
Sigma
346
347348
determine the effect of varying the parameters of a linear programming problem
find multiple solutions, where possible, to a linear programming problem
give the advantages and disadvantages of the Newton-Raphson method or the
bisection method
378
derive the formulae for the Newton-Raphson method
375
give a geometric description of the Newton-Raphson method
375376
give a geometric description of the bisection method
372
Use of appropriate technology is expected.
Achievement Standard Statistics and Modelling 3.5
Complete a statistical investigation involving bi-variate data
3 Credits
Internal
Achievement:
I can
Nulake
Booklet
Nulake
Booklet
Nulake
Booklet
Plan and carry out an investigation involving bi-variate continuous data, analyse the
data and report the findings, including:
a purpose statement
identification of appropriate variables
a description of the data collection method or data source
Use regression to explore the relationship between pairs of variables.
Write a report that
is related to the context
addresses the purpose of the investigation
describes the relationship between at least one pair of variables
I can
carry out an in-depth analysis of bi-variate data within an investigation
analyse bi-variate data by establishing a model using regression
Merit:
discussing the appropriateness of the model established
interpret regression analysis and correlation coefficients (which may involve
comparison of the relationship between more than one pair of variables)
make predictions from regression equations (interpolation and/or extrapolation)
improve regression models, eg consider the effect of outliers, fitting piecewise or nonlinear models
understand the difference between correlation and causality.
write a report that is consistent with the analysis.
I can
critically evaluate an investigation referring to limitations
Excellence
critically evaluate an investigation referring to possible improvements
critically evaluate an investigation referring to justification of method
critically evaluate an investigation referring to alternative approaches
critically evaluate an investigation referring to assumptions made
critically evaluate an investigation referring to potential sources of bias
critically evaluate an investigation referring to relevance and usefulness of evidence
critically evaluate an investigation referring to how widely the findings can be applied
The use of appropriate technology for exploration of data and communication of findings is expected.
This achievement standard does not assess sampling concepts or the use of confidence intervals (see
AS90288, Mathematics 2.5, and AS90642, Statistics 3.2
Achievement Standard Statistics and Modelling 3.6
Achievement:
Use probability distribution models to solve straightforward problems
4 Credits
External
I can
Nulake
Sigma
solve straightforward problems using the binomial distribution
P264-271
Ex 5.1-5.4
solve straightforward problems using the Poisson distribution
P272-276
Ex 6.1-6.2
solve straightforward problems using the normal distribution
P277-288
Ex7.1-7.3
calculate sample statistics to estimate  for a binomial distribution
Ex 5.5
calculate sample statistics to estimate  for a Poisson distribution
P276
calculate probabilities using formulae
P266,273
Excellence
Merit:
use basic sigma notation
Ex 6.3
Ex 5.1,6.1
Ex 16.6
I can
Nulake
use probability distribution models to solve problems involving sums, and
other linear combinations, of normally distributed independent variables
P304-306
Ex 7.6
solve inverse normal problems
P289-293
Ex 7.4
I can
Nulake
Sigma
use and justify probability distribution models to find a parameter given a
probability
P307-311
Ex7.4-7.5
Ex6.4,5.5
select and justifying the use of a model or approximation
P307-311
Ex 8.4
use and justify probability distribution models to approximate a distribution
P307-311
Ex 8.1-8.4
use a continuity correction where a discrete distribution is approximated by
a continuous distribution
P298-303
Ex 8.1,8.3
use sigma notation in calculations or proofs
Sigma
Achievement Standard Statistics and Modelling 3.7
Use a mathematical model involving curve fitting to solve a problem
3 Credits
Internal
Achievement:
I can
use y = ax
Nulake
n
as a mathematical model to solve a problem given the model.
use y = amx as a mathematical model to solve a problem given the model.
use y = Aekt as a mathematical model to solve a problem given the model.
I can
use a power function as an appropriate mathematical model to solve a problem.
use a exponential function as an appropriate mathematical model to solve a problem.
Merit:
p334335
graph the model
select a model to test
I can
justify the choice of mathematical model to solve a problem.
p312
p312
p330331
p312
Ch & Pg no.
p334335
p330331
use a piecewise function as an appropriate mathematical model to solve a problem.
determine the equation of the model
Sigma
p312
p312
p312
p337,
341342
p315347
p343347
p312
p312
p312
Ch & Pg no.
p343347
Excellence
relate the solution to the problem
consider the nature of the underlying variables
consider the possibility of more than one model
p340342
relate the theory behind the model to the given context
discussing limitations of the model
derive the formula for a logarithmic transformation.
p313
Chapter18 from Sigma gives good background information. Chapter 7 from Nulake is the
relevant chapter for this work. Some worksheets and/or additional notes will be given.