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Teacher: CORE AP Statistics
Year: 2014-15
Month: All
Months
Course: AP Statistics
UNIT I: EXPLORING AND UNDERSTANDING DATA (PART A) ~ Lesson 1: Stats Start Here (Introduction)
Lesson 2: Data
Lesson 3: Displaying and Describing Categorical Data
Standards
Essential
Questions
S-IC.1-Understand statistics as a
What is (are)
process for making inferences about statistics, and how
population parameters based on a does this course
random sample from that
relate to life?
population.
S-MD.1-(+) Define a random variable What is (are) data,
for a quantity of interest by assigning and how should
a numerical value to each event in a data be analyzed?
sample space; graph the
corresponding probability
distribution using the same graphical
displays as for data distributions.
Assessments Skills
Content
Lessons
Resources
Intro Quiz 1A
10/1/2014
gain a general understanding of what statistics are and how the course will
progress
statistics
data
variation
Lesson 1: Stats
Start Here
(Introduction)
Textbook - Stats:
Modeling The
World (Pearson)
pgs. 2-6
Quiz 2A
identify and describe the Who, What, When, Where, Why, and How of data, or
recognize when some of this information has not been provided
content
data
data table
case
population
sample
variable
units
categorical variable
quantitative variable
Lesson 2: Data
Pearson Text pgs.
7-19
Quiz 2B
identify the cases and variables in any data set
Lesson 2 Test
identify the population from which a sample was chosen
classify a variable as categorical or quantitative, depending on its use
S-IC.1-Understand statistics as a
process for making inferences about
population parameters based on a
random sample from that
population.
S-ID.5-Summarize categorical data
for two categories in two-way
frequency tables. Interpret relative
frequencies in the context of the
data (including joint, marginal, and
conditional relative frequencies).
Recognize possible associations and
trends in the data.
What are different Quiz 3A
methods of
displaying and
Quiz 3B
describing
categorical data, Lesson 3 Test
and what are the
advantages of
each method?
identify (for any quantitative variable) the units in which the variable has been
measured (or note that they have not been provided)
recognize when a variable is categorical and choose an appropriate display for it frequency table
Lesson 3:
Pearson Text pgs.
distribution
Displaying and 20-43
examine the association between categorical variables by comparing conditional area principle
Describing
and marginal percentages
bar chart
Categorical Data
pie chart
summarize the distribution of a categorical variable with a frequency table
categorical data
display the distribution of a categorical variable with a bar chart or a pie chart
condition
contingency table
make and examine a contingency table
marginal distribution
conditional distribution
make and examine displays of the conditional distributions of one variable for
independence
two or more groups
segmented bar chart
Simpson's paradox
describe the distribution of a categorical variable in terms of its possible values
and relative frequencies
describe any anomalies or extraordinary features revealed by the display of a
variable
describe and discuss patterns found in a contingency table and associated
displays of conditional distributions
UNIT I: EXPLORING AND UNDERSTANDING DATA (PART B) ~ Lesson 4: Displaying and Summarizing Quantitative Data
Lesson 5: Understanding and Comparing Distributions
Lesson 6: The Standard Deviation as a Ruler and the Normal Model
Standards
Essential
Questions
Assessments Skills
S-ID.1-Represent data with
What do different
Quiz 4A
plots on the real number line displays of distribution
(dot plots, histograms, and
show us about the
Quiz 4B
box plots).
center and spread of
S-ID.2-Use statistics
real-life quantitative Lesson 4 Test
appropriate to the shape of data, such as
the data distribution to
earthquake
compare center (median,
magnitudes?
mean) and spread
(interquartile range, standard
deviation) of two or more
different data sets.
S-ID.3-Interpret differences in
shape, center, and spread in
the context of the data sets,
accounting for possible effects
of extreme data points
(outliers).
Content
identify an appropriate display for any quantitative variable
distribution
histogram
guess the shape of the distribution of a variable by knowing something about the data gap
stem-and-leaf plot
select a suitable measure of center and a suitable measure of spread for a variable
dotplot
based on information about its distribution
shape
center
know the basic properties of the median
spread
mode
know the basic properties of the mean
unimodal (bimodal,
multimodal)
know that the standard deviation summarizes how spread out all the data are around uniform
the mean
symmetric
tails
understand that the median and IQR resist the effects of outliers, while the mean and skewed
standard deviation do not
outliers
median
understand that in a skewed distribution, the mean is pulled in the direction of the
range
"skewness" relative to the median
quartile
interquartile range
display the distribution of a quantitative variable with a stem-and-leaf display, a
(IQR)
dotplot, and/or a histogram
percentile
5-number summary
compute the mean and median of a set of data
mean
resistant
compute the standard deviation and IQR of a set of data
variance
standard deviation
describe the distribution of a quantitative variable in terms of its shape, center, and
spread
Lessons
Resources
Lesson 4:
Displaying and
Summarizing
Quantitative
Data
Pearson Text
pgs. 44-79
Lesson 5:
Understanding
and Comparing
Distributions
Pearson Text
pgs. 80-103
describe any anomalies or extraordinary features revealed by the display of a variable
S-ID.1-Represent data with
How can comparing
Quiz 5A
plots on the real number line distributions and
(dot plots, histograms, and
looking at patterns
Quiz 5B
box plots).
over time help us
S-ID.3-Interpret differences in achieve a greater
Lesson 5 Test
shape, center, and spread in understanding of
the context of the data sets, topics like climate and
accounting for possible effects ecology?
of extreme data points
(outliers).
describe summary measures in a sentence
select a suitable display for comparing groups
understand that how data is grouped can affect what kinds of patterns and
relationships are likely to be seen
boxplot
outlier
far outlier
select groupings to show the information that is important for analysis
be aware of the effects of skewness and outliers on measures of center and spread
select appropriate measures for comparing groups based on their displayed
distributions
comparing
distributions
comparing boxplots
time plot
understand that outliers can emerge at different groupings of data and they deserve
special attention
recognize when it is appropriate to make a timeplot
make side-by-side histograms on comparable scales to compare the distributions of
two groups
make side-by-side boxplots to compare the distributions of two or more groups
describe the differences among groups in terms of patterns and changes in their
center, spread, shape, and unusual values
make a time plot of data that have been measured over time
compare the distributions of two or more groups by comparing their shapes, centers,
and spreads
describe trends and patterns in the centers and spreads of groups--especially if there
is a natural order to the groups, such as time
discuss patterns in a timeplot in terms of both the general trend of the data and the
changes in how spread out the pattern is
be cautious about assuming that trends over time will continue into the future
describe the distribution of a quantitative variable in terms of its shape, center, and
spread
describe any anomalies or extraordinary features revealed by the display of a variable
describe patterns over time shown in a timeplot
S-ID.2-Use statistics
How can standard
Quiz 6A
appropriate to the shape of deviation and the
the data distribution to
normal model help us Quiz 6B
compare center (median,
when comparing data
mean) and spread
that does not have the Lesson 6 Test
(interquartile range, standard same units, like
deviation) of two or more
Olympic events?
different data sets.
S-ID.3-Interpret differences in
shape, center, and spread in
the context of the data sets,
accounting for possible effects
of extreme data points
(outliers).
discuss any outliers in the data, noting how they deviate from the overall pattern of
the data
understand how adding (subtracting) a constant or multiplying (dividing) by a constant standardizing
changes the center and/or spread of a variable
standardized value
recognize when standardization can be used to compare values
shifting
understand that standardizing uses the standard deviation as a ruler
rescaling
recognize when a normal model is appropriate
normal model
calculate the z-score of an observation
parameter
compare the values of two different variables using their z-scores
statistic
use the normal models and the 68-95-99.7 rule to estimate the percentage of
observations falling within 1, 2, or 3 standard deviations of the mean
z-score
find the percentage of observations falling below any value in a normal model using a standard normal
normal table or appropriate technology
model
Lesson 6: The
Standard
Deviation as a
Ruler and the
Normal Model
Pearson Text
pgs. 104-134
check whether a variable satisfies the near normal condition by making a normal
probability plot or a histogram
know what z-scores mean
explain how extraordinary a standardized value may be by using a normal model
nearly normal
condition
68-95-99.7 rule
normal percentile
normal probability
plot
UNIT II: EXPLORING RELATIONSHIPS BETWEEN VARIABLES ~ Lesson 7: Scatterplots, Association, and Correlation
Lesson 8: Linear Regression
Lesson 9: Regression Wisdom
Lesson 10: Re-expressing Data
Standards
S-ID.6-Represent data on two
quantitative variables on a
scatter plot, and describe how
the variables are related.
S-ID.8-Compute (using
technology) and interpret the
correlation coefficient of a
linear fit.
Essential
Questions
Assessments Skills
How can scatterplots be Quiz 7A
used to suggest an
association between
Lesson 7 Test
two variables when
observing weather
patterns?
recognize when interest in the pattern of a possible relationship between two
quantitative variables suggests making a scatterplot
Content
Lessons
Resources
scatterplots
Lesson 7:
Scatterplots,
Association, and
Correlation
Pearson Text
pgs. 146-170
outlier
identify the roles of the variables and understand the placing of the response
variable (y-axis) and explanatory variable (x-axis)
response variable
know the conditions for correlation and how to check them
explanatory variable
know that correlations are between -1 and +1, and that each extreme indicates a x-variable
perfect linear association
y-variable
understand how the magnitude of the correlation reflects the strength of a linear
association as viewed in a scatterplot
correlation coefficient
know that correlation has no units
know that the correlation coefficient is not changed by changing the center or
scale of either variable
understand that causation cannot be demonstrated by a scatterplot or correlation
make a scatterplot by hand (for a small set of data) or with technology
compute the correlation of two variables
read a correlation table produced by a statistics program
describe the direction, form, and strength of a scatterplot
identify and describe points that deviate from the overall pattern
use correlation as part of the description of a scatterplot
be alert to misinterpretations of correlation
understand the dangers of suggesting causal relationships when describing
correlations
lurking variable
S-ID.6b-Informally assess the
fit of a function by plotting and
analyzing residuals.
S-ID.6c-Fit a linear function for
a scatter plot that suggests a
linear association.
How can a linear
Quiz 8A
regression be used to Quiz 8B
describe a relationship
between two variables, Lesson 8 Test
like protein and fat
content of items on a
fast food menu?
identify response (y) and explanatory (x) variables in context
model
understand how a linear equation summarizes the relationship between two
variables
linear model
Lesson 8: Linear
Regression
Pearson Text
pgs. 171-200
Lesson 9:
Regression
Wisdom
Pearson Text
pgs. 201-221
predicted value
recognize when a regression should be used to summarize the linear relationship
between two quantitative variables
residuals
judge whether the slope of a regression makes sense
least squares
examine data for violations of the "straight enough condition" that would make it regression to the
inappropriate to compute a regression
mean
understand that least squares slope is easily affected by extreme values
have an understanding of residuals and the least squares criterion
use a plot of residuals against predicted values to check the "straight enough
condition", the "does the plot thicken? condition", and the "outlier condition."
regression line (line of
best fit)
slope
intercept
understand how the standard deviation of the residuals, se, measures variability
around the line
find a regression equation from the summary statistics for each variable and the
correlation between the variables
se
R2
find a regression equation using statistics software, and find the slope and
intercept values in the regression output table
use regression to predict a value of y for a given x
compute the residual for each data value and display the residuals
write a sentence explaining what a linear equation says about the relationship
between y and x, basing it on the fact that the slope is given in y-units per x-unit
understand how the correlation coefficient and the regression slope are related
describe a prediction made from a regression equation, relating the predicted
value to the specified x-value
S-ID.6a-Fit a function to the
data; use functions fitted to
data to solve problems in the
context of the data. Use given
functions or choose a function
suggested by the context.
Emphasize linear, quadratic,
and exponential models.
How can residuals, high- Quiz 9A
leverage points, and
influential points affect Lesson 9 Test
regression models in
marketing situations?
write a sentence interpreting se as representing typical errors in predictions
understand that linear models and linear regression cannot be used if the
underlying relationship between the variables is not itself linear
understand that data used to find a model must be homogeneous
extrapolation
outlier
know the danger of extrapolating beyond the range of the x-values used to find leverage
the linear model, especially when the extrapolation tries to predict into the future
influential point
understand that points can be unusual by having large residual or by having high
leverage
lurking variable
understand that an influential point can change the slope and intercept of the
regression line
look for lurking variables whenever considering the association between two
variables
understand that a strong association does not mean that variables are causally
related
display residuals from a linear model by making a scatterplot of residuals against
predicted values, and know what patterns to look for in the picture
look for high-leverage and influential points by examining a scatterplot of the data
understand how fitting a regression line with and without influential points can
add to the understanding of the regression model
look for high-leverage points by examining the distribution of the x-values, and
understand how they can affect a linear model
include diagnostic information such as plots of residuals and leverages as part of a
report of a regression
report any hig-leverage points
report any outliers, and consider reporting analyses with and without outliers to
assess their influence on the regression
include appropriate cautions about extrapolation when reporting predictions from
a linear model
S-ID.9-Distinguish between
correlation and causation.
S-ID.6a-Fit a function to the
data; use functions fitted to
data to solve problems in the
context of the data. Use given
functions or choose a function
suggested by the context.
Emphasize linear, quadratic,
and exponential models.
How can re-expressing Quiz 10A
data sometimes lead to
more useful regression Lesson 10 Test
models in real-life
situations such as
calculating fuel
efficiency?
discuss possible lurking values
recognize when a well-chosen re-expression may help to improve and simplify an re-expression
analysis
ladder of powers
understand the value of re-expressing data to improve symmetry, to make the
scatter around a line more constant, or to make a scatterplot more linear
recognize when the pattern of the data indicates that no re-expression can
improve the structure of the data
re-express data with powers, and find an effective re-expression for data using
statistics software or a calculator
reverse any of the common re-expressions to put a predicted value or residual
back into the original units
describe a summary or display of a re-expressed variable, making clear how it was
re-expressed and giving its re-expressed units
describe a regression model fit to re-expressed data in terms of the re-expressed
variables
Lesson 10: Reexpressing Data
Pearson Text
pgs. 222-244
UNIT III: GATHERING DATA ~ Lesson 11: Understanding Randomness
Lesson 12: Sample Surveys
Lesson 13: Experiments and Observational Studies
Standards
Essential
Questions
Assessments
S-IC.2-Decide if a specified
How can a simulation Quiz 11A
model is consistent with results model help us to
from a given data-generating investigate real-life
Lesson 11 Test
process, e.g., using simulation. random events, such as
S-MD.6-(+) Use probabilities to casino games?
make fair decisions (e.g.,
drawing by lots, using a
random number generator).
S-IC.3-Recognize the purposes
of and differences among
sample surveys, experiments,
and observational studies;
explain how randomization
relates to each.
S-IC.5-Use data from a
randomized experiment to
compare two treatments; use
simulations to decide if
differences between
parameters are significant.
How can a random
Quiz 12A
sample be used to help
tell us important
Quiz 12B
information about an
entire population, such Lesson 12 Test
as is used in surveys?
Skills
recognize random outcomes in a real-world situation
Content
random
generating random
recognize when a simulation might usefully model random behavior in the numbers
real world
simulation
simulation
perform a simulation by many different means (computer, calculator, dice component
spinner, table of random numbers)
trial
response variable
describe a simulation so that others can repeat it
discuss the results of a simulation study and draw conclusions about the
question being investigated
know the basic concepts and terminology of sampling
Lessons
Resources
Lesson 11:
Understanding
Randomness
Pearson Text
pgs. 255-267
population
Lesson 12: Sample
sample
Surveys
recognize population parameters in descriptions of populations and
sample survey
samples
bias
randomization
understand the value of randomization as a defense against bias
sample size
census
understand the value of sampling to estimate population parameters from population
statistics calculated on representative samples drawn from the population parameter
sample statistic
understand that the size of the sample (not the fraction of the population) representative
determines the precision of estimates
simple random
sample (SRS)
draw a simple random sample from a master list of a population, using a
sampling frame
computer or a table of random numbers
sampling variability
stratified random
know what to report about a sample as part of an account of statistical
sample
analysis
cluster sample
multistage sample
report possible sources of bias in sampling methods
systematic sample
pilot
recognize voluntary response and nonresponse as sources of bias in a
voluntary response
sample survey
bias
convenience sample
under coverage
nonresponse bias
response bias
Pearson Text
pgs. 268-291
S-IC.3-Recognize the purposes
of and differences among
sample surveys, experiments,
and observational studies;
explain how randomization
relates to each.
S-IC.5-Use data from a
randomized experiment to
compare two treatments; use
simulations to decide if
differences between
parameters are significant.
S-IC.6-Evaluate reports based
on data.
What kind of valuable Quiz 13A
information can be
found through
Quiz 13B
experiments and
observational studies in Lesson 13 Test
relation to student
success in school?
recognize when an observational study would be appropriate
identify observational studies as retrospective or prospective, and
understand the strengths and weaknesses of each method
explain the four basic principles of sound experimental design--control,
randomize, replicate, and block
recognize the factors, the treatments, and the response variable in a
description of a designed experiment
observational study Lesson 13:
Experiments and
retrospective study Observational
Studies
prospective study
experiment
random assignment
factor
understand the essential importance of randomization in assigning
treatments to experimental units
understand the importance of replication to move from anecdotes to
general conclusions
response
experimental units
level
understand the value of blocking so that variability due to differences in
attributes of the subjects can be removed
treatment
understand the importance of a control group and the need for a placebo
treatment in some studies
principles of
experimental design
understand the importance of blinding and double-blinding in studies on statistically
human subjects, and be able to identify blinding and the need for blinding significant
in experiments
control group
design a completely randomized experiment to test the effect of a single
factor
blinding
design an experiment in which blocking is used to reduce variation
single-blind
use graphical displays to compare responses for different treatment groups double-blind
properly report the results of an observational study
placebo
compare the responses in different treatment groups to assess whether the placebo effect
differences are larger than could be reasonably expected from ordinary
sampling variability
blocking
properly report the results of an experiment
matching
understand that the description of an experiment should be sufficient for
another researcher to replicate the study with the same methods
designs
confounding
report on the statistical significance of the result in terms of whether the
observed group-to-group differences are larger than could be expected
from ordinary sampling variation
Pearson Text
pgs. 292-316
UNIT IV: RANDOMNESS AND PROBABILITY (PART A) ~ Lesson 14: From Randomness to Probability
Lesson 15: Probability Rules
Standards
Essential
Questions
Assessments
S-CP.1-(+) Define a random
How can the
Quiz 14A
variable for a quantity of
observation of random
interest by assigning a
phenomena (such as
Quiz 14B
numerical value to each event with traffic patterns)
in a sample space; graph the lead us to some very
Lesson 14 Test
corresponding probability
consistent and
distribution using the same
predictable outcomes?
graphical displays as for data
distributions.
S-CP.8-(+) Apply the general
Multiplication Rule in a uniform
probability model, P(A and B) =
P(A)P(B|A) = P(B)P(A|B), and
interpret the answer in terms
of the model.
S-CP.9-(+) Use permutations
and combinations to compute
probabilities of compound
events and solve problems.
S-MD.7-(+) Analyze decisions
and strategies using probability
concepts (e.g., product testing,
medical testing, pulling a
hockey goalie at the end of a
game).
S-MD.1-(+) Define a random
variable for a quantity of
interest by assigning a
numerical value to each event
in a sample space; graph the
corresponding probability
distribution using the same
graphical displays as for data
distributions.
How can an
understanding of the
general rules of
probability lead us to
more accurate
predictions of realworld events?
Quiz 15A
Skills
Content
understand that random phenomena are unpredictable in the short term,
but show long-run regularity
Lessons
random
Lesson 14: From
phenomenon
Randomness to
trial
Probability
recognize random outcomes in a real-world situation
outcome
event
know that the relative frequency of a random event settles down to a value sample space
called the (empirical) probability
Law of Large
Numbers
know the basic definitions and rules of probability
independence
probability
recognize when events are disjoint and when events are independent, and empirical probability
also understand the difference
theoretical
probability
use the facts about probability to determine whether an assignment of
personal probability
probabilities is legitimate
The Probability
Assignment Rule
know how and when to apply the Addition, Multiplication, and
Complement Rule
Complement Rules
disjoint (mutually
exclusive)
use statements about probability in describing a random phenomenon
Addition Rule
legitimate probability
use the terms "sample space", "disjoint events", and "independent events" assignment
correctly
Multiplication Rule
independence
assumption
understand the concept of conditional probability as redefining the Who of General Addition
Lesson 15:
concern, according to the information about the event that is given
Rule
Probability Rules
Quiz 15B
understand the concept of independence
Lesson 15 Test
conditional
probability
know how and when to apply the General Addition and Multiplication Rules
find probabilities for compound events as fractions of counts of
occurrences in a two-way table
make and use a tree diagram to understand conditional probabilities and
reverse conditioning
General
Multiplication Rule
independence (used
formally)
tree diagram
make a clear statement about a conditional probability that conveys how
the condition affects the probability
avoid making statements that assume independence of events when there
is no clear evidence that they are in fact independent
Resources
Pearson Text
pgs. 324-341
Pearson Text
pgs. 342-365
UNIT IV: RANDOMNESS AND PROBABILITY (PART B) ~ Lesson 16: Random Variables
Lesson 17: Probability Models
Standards
S-CP.2-(+) Calculate the expected value
of a random variable; interpret it as the
mean of the probability distribution.
S-CP.3-(+) Develop a probability
distribution for a random variable
defined for a sample space in which
theoretical probabilities can be
calculated; find the expected value.
S-CP.4-(+) Develop a probability
distribution for a random variable
defined for a sample space in which
probabilities are assigned empirically;
find the expected value.
S-CP.5a-Find the expected payoff for a
game of chance.
Essential
Questions
Assessments Skills
How are
Quiz 16A
probability
models and
Lesson 16 Test
random
variables used
by insurance
companies to
determine the
cost of
insurance
premiums?
recognize random variables
Content
Lessons
Resources
random variable
Lesson 16: Random Pearson Text
Variables
pgs. 366-387
understand that random variables must be independent in order to determine discrete random
the variability of their sum or difference by adding variances
variable
find the probability model for a discrete random variable
continuous random
variable
find the mean (expected value) and the variance of a random variable
probability model
use the proper notation when working with population parameters
expected value
determine the new mean and standard deviation after adding a constant,
multiplying by a constant, or adding or subtracting two independent random
variables
variance
standard deviation
interpret the meaning of the expected value and standard deviation of a
random variable in the proper context
changing a random
variable by a constant
adding or subtracting
random variable
S-CP.5-(+) Weigh the possible outcomes How can the Quiz 17A
know how to tell if a situation involves Bernoulli trials
Bernoulli trials
Lesson 17:
Pearson Text
of a decision by assigning probabilities to different types
Probability Models pgs. 388-404
payoff values and finding expected
of probability Lesson 17 Test choose whether to use a geometric or a binomial model for a random variable geometric probability
values.
models be
involving Bernoulli trials
model
S-CP.5b-Evaluate and compare strategies used in
on the basis of expected values.
Bernoulli trials
know the appropriate conditions for using a geometric, binomial, or normal
binomial probability
to reach
model
model
reasonable
approximations
find the expected value of a geometric model
10% condition
in real-world
situations?
calculate geometric probabilities
success/failure
condition
find the mean and standard deviation of a binomial model
calculate binomial probabilities, perhaps approximating with a normal model
interpret means, standard deviations, and probabilities in the Bernoulli trial
context
UNIT V: FROM THE DATA AT HAND TO THE WORLD AT LARGE (PART A) ~ Lesson 18: Sampling Distribution Models
Lesson 19: Confidence Intervals for Proportions
Essential
Questions
Standards
S-IC.1-Understand statistics as a process
for making inferences about population
parameters based on a random sample
from that population.
S-ID.4-Use the mean and standard
deviation of a data set to fit it to a
normal distribution and to estimate
population percentages. Recognize that
there are data sets for which such a
procedure is not appropriate. Use
calculators, spreadsheets, and tables to
estimate areas under the normal curve.
S-IC.1-Understand statistics as a process
for making inferences about population
parameters based on a random sample
from that population.
S-ID.4-Use the mean and standard
deviation of a data set to fit it to a
normal distribution and to estimate
population percentages. Recognize that
there are data sets for which such a
procedure is not appropriate. Use
calculators, spreadsheets, and tables to
estimate areas under the normal curve.
Assessments Skills
What can a
Quiz 18A
sampling
distribution
Lesson 18 Test
model tell us
about poll
results given to
different
samples of
adults in the
U.S.
population?
understand that the variability of a statistic depends on the size of the sample
understand that the Central Limit Theorem gives the sampling distribution
model of the mean for sufficiently large samples regardless of the underlying
population
Content
Lessons
Resources
sampling distribution
model
Lesson 18:
Sampling
Distribution
Models
Pearson Text
pgs. 412-438
Lesson 19:
Confidence
Intervals for
Proportions
Pearson Text
pgs. 439-458
sampling variability
sampling error
demonstrate a sampling distribution by simulation
use a sampling distribution model to make simple statements about the
distribution of a proportion or mean under repeated sampling
sampling distribution
model for a proportion
Central Limit Theorem
interpret a sampling distribution model as describing the values taken by a
statistic in all possible realizations of a sample or randomized experiment under sampling distribution
the same conditions
model for a mean
How can the Quiz 19A
understand confidence intervals as a balance between the precision and the
standard error
interpretation
certainty of a statement about a model parameter
of a confidence Lesson 19 Test
confidence interval
interval and
understand that the margin of error of a confidence interval for a proportion
standard error
changes with the sample size and the level of confidence
one-proportion zin sample
interval
proportions
examine data for violations of conditions that would make inference about a
help to give us
population proportion unwise or invalid
margin of error
a better
understanding
construct a one-proportion z-interval
critical value
of an entire
population?
interpret a one-proportion z-interval in a simple sentence or two
UNIT V: FROM THE DATA AT HAND TO THE WORLD AT LARGE (PART B) ~ Lesson 20: Testing Hypotheses About Proportions
Lesson 21: More About Tests and Intervals
Lesson 22: Comparing Two Proportions
Standards
S-IC.1-Understand statistics as a
process for making inferences about
population parameters based on a
random sample from that
population.
S-ID.4-Use the mean and standard
deviation of a data set to fit it to a
normal distribution and to estimate
population percentages. Recognize
that there are data sets for which
such a procedure is not appropriate.
Use calculators, spreadsheets, and
tables to estimate areas under the
normal curve.
Essential
Questions
Assessments Skills
How can we
Quiz 20A
create and test
hypotheses about Lesson 20 Test
the effectiveness
of money spent on
advertising a
product on
television?
Content
Lessons
state the null and alternative hypotheses for a one-proportion z-test
null hypothesis
know the conditions that must be true for a one-proportion z-test to be
appropriate, and know how to examine data for violations of those conditions
alternative
hypothesis
Lesson 20: Testing Pearson Text
Hypotheses About pgs. 459-479
Proportions
identify and use the alternative hypothesis when testing hypotheses
two-sided (twotailed) alternative
understand how to choose between a one-sided and two-sided alternative
hypothesis, and be able to explain the choice
one-sided (onetailed) alternative
perform a one-proportion z-test
P-value
write a sentence interpreting the results of a one-proportion z-test
interpret the meaning of a P-value in nontechnical language
one-proportion ztest
Resources
S-IC.1-Understand statistics as a
process for making inferences about
population parameters based on a
random sample from that
population.
S-ID.4-Use the mean and standard
deviation of a data set to fit it to a
normal distribution and to estimate
population percentages. Recognize
that there are data sets for which
such a procedure is not appropriate.
Use calculators, spreadsheets, and
tables to estimate areas under the
normal curve.
How can
Quiz 21A
understand that statistical significance does not measure the importance or
hypothesis testing
magnitude of an effect, and recognize when others misinterpret statistical
and awareness of Quiz 21B
significance
errors help us to
better understand Lesson 21 Test understand the close relationship between hypothesis tests and confidence
the risks
intervals
associated with
the side effects of
identify and use the alternative hypothesis when testing hypotheses
prescription
drugs?
understand how the critical value for a test is related to the specified alpha level
alpha level
statistically
significant
Lesson 21: More
About Tests and
Intervals
Pearson Text
pgs. 480-503
significance level
type I error
type II error
understand that the power of a test gives the probability that it correctly rejects power
a false null hypothesis when a specified alternative is true
effect size
understand that the power of a test depends in part on the sample size
complete a hypothesis test for a population proportion
interpret the meaning of a P-value in nontechnical language
understand that the P-value of a test does not give the probability that the null
hypothesis is correct
know that a null hypothesis is not "accepted" if it cannot be rejected, but rather
it is only "failed to be rejected" for lack of evidence against it
S-IC.1-Understand statistics as a
How can the
Quiz 22A
state the null and alternative hypotheses for testing the difference between two variances of
Lesson 22:
process for making inferences about analysis of two
population proportions
independent random Comparing Two
population parameters based on a population
Quiz 22B
variables
Proportions
random sample from that
proportions give
examine data for violations of conditions that would make inference about the
population.
us better
Lesson 22 Test difference between two population proportions unwise or invalid
sampling distribution
S-ID.4-Use the mean and standard information than
of the difference
deviation of a data set to fit it to a one proportion in
understand the formula for the standard error of the difference between two
between two
normal distribution and to estimate the investigating
independent sample proportions
proportions
population percentages. Recognize of traffic
that there are data sets for which
accidents?
find a confidence interval for the difference between two proportions
two-proportion zsuch a procedure is not appropriate.
interval
Use calculators, spreadsheets, and
perform a significance test of the natural null hypothesis that two population
tables to estimate areas under the
proportions are equal
pooling
normal curve.
write a sentence describing what is said about the difference between two
two-proportion zpopulation proportions by a confidence interval
test
write a sentence interpreting the results of a significance test of the null
hypothesis that two population proportions are equal
interpret the meaning of a P-value in nontechnical language, making clear that
the probability claim is made about computed values and not about the
population parameter of interest
know that a null hypothesis is not "accepted" if it fails to be rejected
Pearson Text
pgs. 504-522
UNIT VI: LEARNING ABOUT THE WORLD ~ Lesson 23: Inferences About Means
Lesson 24: Comparing Means
Lesson 25: Paired Samples and Blocks
Standards
Essential
Assessments Skills
Questions
S-IC.1-Understand statistics as a process for
making inferences about population parameters
based on a random sample from that population.
S-ID.4-Use the mean and standard deviation of a
data set to fit it to a normal distribution and to
estimate population percentages. Recognize that
there are data sets for which such a procedure is
not appropriate. Use calculators, spreadsheets,
and tables to estimate areas under the normal
curve.
How can
Quiz 23A
statistical
inferences Quiz 23B
about the
mean help Lesson 23 Test
us when
investigating
data relating
to traffic
safety?
Content
Lessons
know the assumptions required for t-tests and t-based confidence intervals
Student's t
examine data for violations of conditions that would make inference about the
population mean unwise or invalid
degrees of
freedom (df)
Lesson 23:
Pearson Text
Inferences
pgs. 530-559
About Means
understand that a confidence interval and a hypothesis test are essentially equivalent
one-sample tinterval for the
mean
compute and interpret a t-test for the population mean using a statistics package or
working from summary statistics for a sample
compute and interpret a t-based confidence interval for the population mean using a
statistics package or working from summary statistics for a sample
Resources
one-sample ttest for the
mean
explain the meaning of a confidence interval for a population mean
understand that a 95% confidence interval does not trap 95% of the sample values
interpret the result of a test of a hypothesis about a population mean
know not to "accept" a null hypothesis if it cannot be rejected, rather "fail to reject" it
S-IC.1-Understand statistics as a process for
making inferences about population parameters
based on a random sample from that population.
S-ID.4-Use the mean and standard deviation of a
data set to fit it to a normal distribution and to
estimate population percentages. Recognize that
there are data sets for which such a procedure is
not appropriate. Use calculators, spreadsheets,
and tables to estimate areas under the normal
curve.
S-IC.1-Understand statistics as a process for
making inferences about population parameters
based on a random sample from that population.
S-ID.4-Use the mean and standard deviation of a
data set to fit it to a normal distribution and to
estimate population percentages. Recognize that
there are data sets for which such a procedure is
not appropriate. Use calculators, spreadsheets,
and tables to estimate areas under the normal
curve.
How can we Quiz 24A
use
statistical
Lesson 24 Test
inference to
compare the
means of
two
independent
groups, such
as battery
life of
different
brands?
How can we Quiz 25A
use a paired
t-test to
Lesson 25 Test
analyze the
data from
subjects
before and
after a
treatment?
understand that the P-value of a test does not give the probability that the null
hypothesis is correct
recognize situations in which we want to do inference on the difference between the
means of two independent groups
examine data for violations of conditions that would make inference about the
difference between two population means unwise or invalid
recognize when a pooled-t procedure might be appropriate and explain why to use a
two-sample method anyway
two-sample t
methods
Lesson 24:
Comparing
Means
Pearson Text
pgs. 560-586
two-sample tinterval for the
difference
between means
pooling
perform a two-sample t-test using a statistics package or calculator
interpret a test of the null hypothesis that the means of two independent groups are
equal
recognize whether a design that compares two groups is paired
pooled-t
methods
paired data
find a paired confidence interval
paired t-test
perform a paired t-test
paired-t
confidence
interval
interpret a paired t-test
interpret a paired t-interval
Lesson 25:
Pearson Text
Paired
pgs. 587-608
Samples and
Blocks
UNIT VII: INFERENCE WHEN VARIABLES ARE RELATED ~ Lesson 26: Comparing Counts
Lesson 27: Inferences for Regression
Standards
Essential
Questions
Assessments Skills
S-IC.1-Understand statistics as a How can chi-square Quiz 26A
process for making inferences tests give an overall
about population parameters idea of whether an
Quiz 26B
based on a random sample from observed distribution
that population.
differs from a
Lesson 26 Test
hypothesized one?
Content
Lessons Resources
recognize when a test of goodness-of-fit, a test of homogeneity, or a test of
independence would be appropriate for a table of counts
Chi-square model
Lesson 26: Pearson Text
cell
Comparing pgs. 618-648
Chi-square statistic
Counts
understand that the degrees of freedom for a chi-square test depend on the dimensions Chi-square test of
of the table and not on the sample size
goodness-of-fit
Chi-square test of
display and interpret counts in a two-way table
homogeneity
Chi-square test of
use the chi-square tables to perform chi-square tests
independence
Chi-square component
compute a chi-square test using statistics software or a calculator
standardized residual
two-way table
examine the standardized residuals to explain the nature of the deviations from the null contingency table
hypothesis
interpret chi-square as a test of goodness-of-fit in a few sentences
interpret chi-square as a test of homogeneity in a few sentences
interpret chi-square as a test of independence in a few sentences
S-IC.1-Understand statistics as a How are inferences Quiz 27A
understand that the "true" regression line does not fit the population data perfectly, but
process for making inferences for regression used to
rather is an idealized summary of that data
about population parameters make reasonable
Quiz 27B
based on a random sample from assumptions about
examine data and a y vs. x for violations of assumptions that would make inference for
that population.
collected data?
Lesson 27 Test regression unwise or invalid
S-ID.7-Interpret the slope (rate
of change) and the intercept
examine displays of the residuals from a regression to double-check that the conditions
(constant term) of a linear
required for regression have been met
model in the context of the
be careful in checking for failures of the Independence Assumption when working with
data.
data recorded over time
S-ID.6c-Fit a linear function for a
scatter plot that suggests a
test the standard hypothesis that the true regression slope is zero
linear association.
state null and alternative hypotheses
find a confidence interval for the slope of a regression based on the values reported in a
standard regression output table
summarize a regression in words
state the meaning of the true regression slope, the standard error of the estimated
slope, and the standard deviation of the errors
interpret the P-value of the t-statistic for the slope to test the standard null hypothesis
interpret a confidence interval for the slope of a regression
conditions for inferences Lesson 27: Pearson Text
in regression
Inferences pgs. 649-682
for
residual standard
Regression
deviation
t-test for the regression
slope
confidence interval for
the regression slope