NRHS AP Statistics Curriculum
Number Lesson
Requirement
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What is statistics?
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Given a set of data, identify the individuals and variables
(categorical or quantitative).
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Given a set of data, create a dot plot and time plot manually
and using the TI-84
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Create a histogram using class width, class limits, class
boundaries, class midpoints, and relative frequency.
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Interpret histograms.
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Stem and Leaf display find the mean and median and mode.
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How to find the Measures of Central Tendency (center): Mean,
Median, Mode manually and using the TI-84.
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Describe the difference between parameters and statistics with
respect to the mean and standard deviation.
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Have Students using their descriptive statistics sheets that will
be given to them on the AP to compare formulas.
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Given a density graph, Students should be able to calculate the
area under the curve.
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Describe the normal distribution use exactly one, two or three
standard deviations away from the mean to find probabilities.
𝑥−µ
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Use the normal curve using the formula 𝑧 = 𝜎 to find the
exact probabilities of ANY value from the mean. Use the chart
to locate the probability.
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Given the probability or percentile, find 𝑥 (do inverse)
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Define explanatory and response variables, graph, and interpret
scatterplots. Describe outliers and influential points.
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Define correlation and calculate the correlation (𝑟) manually
using statistics descriptive sheet and using TI-84. Describe
strength and direction. Interpret coefficient of determination
(𝑅2).
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Calculate the slope and 𝑦 −intercept to obtain the 𝐿𝑆𝑅𝐿.
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Using the calculated 𝐿𝑆𝑅𝐿 find a predicted 𝑦 for a specified 𝑥.
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Find residuals manually and graphically. Describe what is
implied when the residuals form a pattern and are not
scattered.
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Calculate exponential growth. Find the 𝐿𝑆𝑅𝐿 using logs.
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Calculate power growth. Find the 𝐿𝑆𝑅𝐿.
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Describe simple random sample [SRS] and random number
table.
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How to use the random digit table [RDT] on the AP and how
to set up an experiment, which will be appropriate to use the
RNT. Use TI-84 to conduct simulations (rand button).
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Describe systematic sampling, cluster sampling, convenience
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NRHS AP Statistics Curriculum
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sampling.
Describe a census, sample simulation, observational study,
experimental study, placebo, randomized two treatments
experiment, double-blind experiment, control group,
confounding (lurking variables), randomization, and
replication. Use scenarios to describe surveys nonresponse,
voluntary response, hidden bias, and other bias generalizing
results.
What is probability? Law of large numbers? Discuss important
facts.
Given a sample space, find the probability of an event and the
complement of the event. Use descriptive statistics sheet to
show Students the formulas.
Describe the difference between independent, dependent, and
mutually exclusive events. Use Venn Diagram and formula
sheet.
Multiplication rule—combinations for probability
Definition of discrete random variable and continuous random
variable. Describe the difference between the probability of
less than (<) and less than or equal to (≤) for continuous
random variable.
Find the mean ( 𝐸(𝑥) ) and standard deviation ( 𝜎 )for discrete
probability distribution. Use descriptive statistics sheet to show
Students formula.
Describe the features of a binomial experiment and use the
formula for the binomial probability distribution and using the
TI-84.
Formula for the binomial probability distribution and using the
TI-84.
Find the mean and standard deviation of binomial probability
distributions. Calculate the probability.
Formula for the binomial probability distribution and using the
TI-84.
Describe the features of a geometric probability distribution
Find the mean and standard deviation of geometric probability
distributions.
The central limit theorem: probability regarding 𝑥 and 𝑥̅ . Use z
when 𝑛 ≥ 30.
Sampling distribution for the proportion p. Make inference
about the population 𝑛𝑝>5 and 𝑛𝑞>5.
Find the mean and standard deviation for the proportion.
Estimating mu with large samples. Make inference about 𝜎 and
𝑠. Have Students look up confidence intervals using chart.
Construct a confidence interval for the population mean using
Revised 2015 College Board Approved 2008
NRHS AP Statistics Curriculum
samples.
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Estimating mu with small samples. Students should know the
difference between 𝑧 and 𝑡 with respect to estimating 𝑠. Only
use 𝑠 for 𝑡-distribution. Have Students look up confidence
intervals with 𝑑. 𝑓. = 𝑛 − 1
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Construct a confidence interval for the population mean using
samples. Interpret a confidence interval.
Estimating p for the proportion. Construct a confidence
interval the mean p. Interpret a confidence interval.
Given all information for a set of data with the exception of 𝑛,
find an appropriate sample size (i.e. solve for n)
Given two populations, estimate the difference between the
mean and make inference about the population.
Given two populations, estimate the difference between the
proportion mean
State the Null and Alternate hypotheses. Discuss Type I and
Type II. Discuss level of significance. Discuss one or two
tailed test.
Test involving the mean mu (large samples). Use TI-84 to
assess a test. Discuss critical values for testing, Critical region.
Draw conclusions. Discuss statistical significance.
The 𝑃 −value in Hypothesis Testing identify the meaning of
𝑃 −value for a statistical test. Compute the 𝑃 −value for large
sample tests of µ (mu). Draw test conclusions based on the
𝑃 −values and the level of significance.
Identify the components of a small sample test of µ. Use
degrees of freedom and the 𝑡 −table to find critical values.
Compute the sample test statistic. Estimate the 𝑃 −value for a
small sample test of µ. Draw conclusions using the level of
significance alpha and the 𝑃 −value.
Test involved paired differences (dependent samples)identify
paired data and dependent samples. Explain the advantages of
paired data tests. Compute differences and the sample test
statistic.
Use degree of freedom and the t table to find critical values.
Estimate the P value and conclude the test.
Testing Difference of Two Means identify independent sample
and sampling distribution. Compute the sample test statistic
and 𝑃 −value for µ1 𝑎𝑛𝑑 µ2 (large samples).
Identify independent sample and sampling distribution.
Compute the test statistic and 𝑃 −value for µ1 𝑎𝑛𝑑 µ2 for small
samples.
Compute the test statistic, critical value, and 𝑃 −value for
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𝑝1 𝑎𝑛𝑑 𝑝2. Use the level of significance α and the 𝑃 −value to
conclude test.
Review how to find the LSRL and correlation (𝑟) in the
calculator.
Use 𝑆𝑆𝑥, 𝑆𝑆𝑦, 𝑆𝑆𝑥𝑦, which is equivalent to the variance of
𝑥, 𝑦, 𝑎𝑛𝑑 𝑥𝑦 respectively.
Use the formula to calculate the standard error of estimate.
Calculate the margin of error for 𝑦 −hat at a specified 𝑥.
Construct a confidence interval for 𝑦 −hat.
Find a confidence interval level for the slope of the 𝐿𝑆𝑅𝐿.
Test the slope of 𝐿𝑆𝑅𝐿 to determine if there is a linear
relationship between the explanatory variable and the response
variable.
Students should be able to read minitab output(computer
software).
Compute Chi-Square with one set of data to test “goodness of
fit.”
Use a contingency table to compute the expected frequency of
Chi-Square. Find the number of degrees of freedom(𝑅 −
1) (𝐶 − 1) in a contingency table.
Use TI-84 to determine if there is an association between two
events.
**** Review for AP Exam using practice exams and AP free response problems*****
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Testing and Estimating a Single Variance or Standard Deviation. Set up a test
for a single variance. Compute the Chi Square statistic
Use the Chi-Square statistic distribution to complete the test and estimate a P
value. Compute the confidence intervals for variance and standard deviation.
Set up a test for two variances. Use sample variances to compute the sample F
statistic.
Use the F distribution to complete the test and estimate a P value.
One way ANOVA learn about the risk alpha of a type I error when we test
several means at once
Compute mean squares between groups within groups. Compute the sample F
statistic
Use the F distribution to conclude the test and estimate a P value.
Learn the notation and setup for two-way ANOVA tests
Learn about the three main types of deviations and how they break into
additional effects.
Revised 2015 College Board Approved 2008
NRHS AP Statistics Curriculum
Topic by Topic
I.
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II.
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Linear Regression
Students will be able to create scatter diagrams and determine the correct
correlation given multiple choices.
Students will be able to determine if a correlation is positive, negative or zero.
Students will be able to use their TI-84 plus to enter in their data and find the line
of best.
Students will be able to use their TI-84 plus to find the standard deviations of both
𝑥 and 𝑦 and their slope of the line. They will then plug that information into the
formula to find 𝑟 (the correlation) Students will be able to use the line of best fit
to predict values. They will then use the residual formula and find the residuals of
the data. They will be able to then determine if a line of best fit should be used
according to the pattern. If a line of best fit should not be used, students will
explore quadratics, exponentials, logarithmic and other possible regressions using
their TI 84 plus
Students will be working backwards given the prediction point and the residual to
find the actual and vice versa.
Students will explore what happens to the correlation coefficient when they
switch their x and y values and explore the result of the 𝐿𝑆𝑅𝐿.
Students will then work with the formula of the correlation on the formula sheet
and discuss why this happens.
Students will learn about R2 (the ratio of explained variation over total variation).
Students will be given multiple questions on linear regression from Practice AP
books.
Z-scores
Students will begin by given data and finding the mean, median, and mode.
Students will then be taught how to find the standard deviation using the formula
and what is meant by a standard deviation.
Students will be given questions based on the empirical rule (68-95-99) and will
be asked to interpret the information given.
Students will be given questions that ask about percent that do not fall one, two,
or three standard deviations away
Students will be given charts on z-scores and z-scores will be explained to the
Students.
Students will be begin by just finding the corresponding probability to z-scores
and finding the probability above or below the curve
Students will then be able to use their TI-84 plus to find the standard deviation
along with the mean median and mode.
Students will have questions where they must convert their information to a z-score, look up the z-score and find the probability.
Revised 2015 College Board Approved 2008
NRHS AP Statistics Curriculum
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Students will then have to work backwards given the probability, the must find
the z-score, place it back into the equation given the population mean and
standard deviation to find the mean. (i.e. a student scored 77% on the math
portion of the SATs, if the math portion of the SAT scores are normally
distributed with a µ= 510 and σ = 50, what did the student score?)
Students will learn how to find probabilities and means using their TI-84
calculator
Students will learn how to find probabilities for averages (the central limit
theorem).
Students will be able to find the probability using a z-score given a sample mean
(𝑥̅ ), population mean (µ), population standard deviation (σ) and sample size (𝑛).
Students will then learn about binomial distribution. They will be given the same
data and use the formula µ=𝑛𝑝 and σ= √𝑛𝑝𝑞.
Students will learn about proportions and will then be able to find the mean and
𝑝
𝑝𝑞
standard deviation of the sampling distribution by using the formula 𝑛 and √ 𝑛 to
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III.
find the mean and standard deviation, respectively.
Students will work on various questions to find the mean and standard deviations.
They will then find z-scores and the probabilities corresponding to them.
Students will then be able to compare the central limit theorem to the binomial
distribution as well as sampling distributions for proportions.
Students will use their TI-84 to find the probabilities and compare.
Estimations
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Students will begin this topic by talking about what happens when µ is unknown
but 𝑥̅ is given. We will discuss confidence intervals and their meanings. We will
discuss the meaning of 90%, 95%, 98%, 99% confidence intervals and levels.
Students will then take the 𝑧 −score formula and place it between two critical
𝜎
values to form 𝑥̅ ± 𝑧 𝑛
√
𝜎
Students will solve for µ and will be left with 𝑥̅ ± 𝑧 𝑛. Students will discuss the
√
margin of error and what it means in terms of the population.
Students will begin working on problems and creating confidence intervals so
they can estimate where µ (when σ is known) and how confident we are we then
will turn to estimating mu when σ is unknown. We will replace the z- critical
value with t-critical value. Students already know how to find the t-value. We
will continue to work on problems when sample sizes are small and the sample
standard deviation is unknown.
Students will move on and find out what is the appropriate sample size to choose
given the margin of error that is wanted.
Students will do interpretations of both confidence intervals and confidence levels
and have multiple choice questions on what is the correct interpretation of
confidence intervals and confidence levels.
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NRHS AP Statistics Curriculum
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Students will distinguish between independent samples (such as basketball
players salaries and football players salaries) and dependent samples (such as
amount of fish before a fire and after a fire).
Students will compute an interval for the difference between µ1-µ2 when the
standard deviations are known (𝑧 −score) and the standard deviations are
𝜎2
𝜎2
1
2
unknown (𝑡 −score). Students will use the formula 𝑥̅1 − 𝑥̅2 ± zc √𝑛 + 𝑛
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IV.
Students will create a confidence interval and interpret based on the intervals
signs (i.e. if the interval is positive, one can conclude µ1 > µ2 and if the interval
is negative µ1 < µ2
Students will also be able to also work on two proportions using the formulas.
Use the TI-84 go to STAT –TEST and we will work on 𝑧 −interval, 𝑡 −interval, 2−sample 𝑧 −interval 2-sample 𝑡 −interval, 1 −prop 𝑧 −interval, 2 −prop
𝑧 −interval
Students will work on various questions for AP review books
Hypothesis Testing
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Students will understand the rationale for statistical tests and that it is designed to
assess the strength of the evidence (data)
Students will begin by stating the null hypothesis (the statement under
investigation or being tested). They will understand that this is the statement that
says things are the same.
Students will then state an alternative hypothesis (this is the statement Students
will use to try to reject the null hypothesis
Students will learn about type I and type II errors based on examples such as
courtroom where a judge makes the correct decision (no error) or if it was true
and rejected (type I error) and if it was false and not rejected (type II error) or
false and rejected was a correct decision
Students will learn about the level of significance alpha is the probability of
rejecting null hypothesis when it is true. Students will learn the three types of tests
(left-tailed that is the parameter is less than the claimed null hypothesis, the right-tailed is the parameter that is more than the claimed null hypothesis, and two-tailed that the claim is different)
Students will learn about 90 95 98 99 percent corresponding z scores of 1.645,
1.96, 2.33, 2.58 and then find the P values that correspond to it. P-values of 5% or
1% will be explained. Students will see how the critical values go hand-in-hand
with the p-values.
Students will state a p-value first then begin the problem given. The will find a zscore and look up the z-score to find the corresponding probability. They will then
compare this to the p-value. If the probability that was just found is smaller than
the p-value, they will reject the null hypothesis. Otherwise there is not sufficient
evidence to reject. Students will also have to memorize the 1% and 5% z-scores
for left, right and two-sided tail. They will begin the problem and find a z test.
Revised 2015 College Board Approved 2008
NRHS AP Statistics Curriculum
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Then just compare it to 1.645 1.96 2.33 2.58 then determine if the null hypothesis
is rejected or failed to reject.
Students will then do the same for a proportion 𝑝.
Students will continue on tests involving paired differences (dependent samples).
They will place their data into the calculator and subtract L2 from L1 and place
those answers in L3. They will find the mean, sample standard deviation and n
and compute a t-statistic. They will then determine whether they reject or fail to
reject the null hypothesis. Example: 10 students taking the SATs then taking a
prep course then taking the SATs again. Find the difference in the exams and
determine if the course made a difference or not.
Students will then work on tests involving independent samples. They will use the
𝑥̅ −𝑥̅
formula 𝑧= 𝜎12 𝜎22
√
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+
𝑛1 𝑛2
Students will then be able to determine if they should reject the null hypothesis or
not. The same is done with proportions.
Students will make the right interpretation at the end. (if the example was two
types of teaching methods and the p-value was less than 5% we can concluded at
the 5% level of significance there is sufficient evidence to show that the second
teaching method increased the population mean score on the exam.
Students' notebooks are divided by topics. Students now will have to do the same
questions using confidence intervals. They will look at µ and determine if µ is in
the interval. They will see how confidence intervals and hypothesis testing are
interchangeable, and how using a confidence interval, students could reject or fail
to reject the null hypothesis.
With smaller samples students will learn about pooled standard deviation.
Example: suppose the sample values of standard deviations 𝑠1 𝑎𝑛𝑑 𝑠2 are
sufficiently close and that there is reason to believe the population standard
deviations are equal then you can use the pooled standard deviation.
Chi-squared
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Students will set up a test to investigate whether a distribution is a “good fit” or
not.
Students will have an overview of chi-squared distribution (𝜒 2 ) (learn how to
read the chart, right-skewed, degrees of freedom, etc.).
Students will learn about contingency tables and will have observed values in a
single row. They will then find the expected value and place it in the row below it.
𝛴(𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑−𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑)2
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Students will find the 𝜒 2 test statistic using the formula
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Students will also work on examples for the “goodness of fit” such as what is
most important (vacation, salary, etc) to workers during the year 2008 and
determining if that importance stayed the same—a “good fit” the year 2012. They
will then look at the chart with 𝑛 − 1 degrees of freedom and determine if the two
events are independent (example could be keyboard arrangement and learning
times)
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑
Revised 2015 College Board Approved 2008
NRHS AP Statistics Curriculum
Students will then move to 𝑛 X 𝑚 contingency tables where the expected for each cell is
𝑅𝑜𝑤 𝑇𝑜𝑡𝑎𝑙∗𝐶𝑜𝑙𝑢𝑚𝑛 𝑇𝑜𝑡𝑎𝑙
found by using the formula ( 𝑇𝑜𝑡𝑎𝑙 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 ). Students will then do 𝜒 2 then
compare to the 𝑃 −value. (An example could be types of soda students drink and the
school level –high school or elementary school).
Students will also have to find between what two 𝑃 −values the 𝜒 2 falls between.
VI.
Randomization
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Students will set up learn about randomization and be given a random digit table
[RDT].
Students will learn how to number things 0 − 9, 01 − 10, 001 − 100 etc. and
read off digits to choose their samples randomly.
We will then set up experiments so randomness is used.
Example 1: Imagine you have to use three homes for questioning on a street that
has 10 homes. Students will number the homes 0-9 and read off single digits until
they find the first three homes. Those three homes will be used for the interview.
Example 2: Let’s assume that we wanted to see if the NYC homes have deadbolts
and we knew that 75% of homes in NYC had deadbolts. We wanted to see if 10
homes we went to had deadbolts. Students will learn that they can number homes
as follows: 00-74 are homes with deadbolts and 75-99 without. They will read
from the RDT and find the first ten homes and see who has the deadbolts and
compare it to the actual.
Students will learn many terminologies such as double-blinding, SRS,
experiments, response variables, explanatory variables, voluntary response,
question wording etc.
Students will be given paragraphs of certain situations and will have to locate bias
in the paragraphs. They will also have to rewrite paragraphs and tell me what they
could do to make it as unbiased as possible
VII. Probability
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Students will learn about Probability as what we want divided by total. They will
learn about compliment (the probability of rain is .4 the probability of not rain is
.6)
Students will be introduced to two or more events
Students will learn about “or” and “and” statements.
Students will learn about independent and dependent probabilities.
Students will learn about the following formulas:
𝑃(𝐴 𝑈 𝐵) = 𝑃 (𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵).
𝑃(𝐴 ∩ 𝐵) = 𝑃 (𝐴) ∗ 𝑃(𝐵) if the events are independent.
𝑃(𝐴 ∩ 𝐵) = 0 if the events are mutually exclusive.
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NRHS AP Statistics Curriculum
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴)𝑃(𝐵|𝐴) for a conditional probability.
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Students will learn about mutually exclusive (picking a red marble and a green
marble at the same time, passing and failing the same test)
Students will deal with given statements. They will make tree diagrams and find
probabilities. Examples will be testing positive for a disease is 30% and actually
having the disease is 98%. If someone doesn’t have the disease, the probability
having it is 3%. Find the probability of having the disease given the test positive.
Revised 2015 College Board Approved 2008