> VXUW 3bjbj,, XFaFa+Tp)dpppppKB,((((((($*-v)KK)pp*)pp((['(psw("(@)0p)("..D(.( ))p).BJ: Roanoke Valley Governors School for Science and Technology
AP Statistics
Competency List
(Last updated: August 2016)
Course description for AP Statistics:
AP/College Statistics emphasizes interdisciplinary applications built around four broad conceptual themes of exploring data, planning a study, anticipating patterns, and statistical inference. The topics include descriptive statistics, elementary probability, probability distributions, estimation, hypothesis testing, correlation and regression, analysis of variance, chi-square test, non-parametric methods, the calculus foundation of properties and formulas. Students are expected to obtain a qualifying score of 3, 4, or 5 on the AP Statistics exam at the end of this course.
This course is taught using best practices in gifted education. Each competency is aligned with
Hocketts five principles of gifted education:
Gifted Education Principles:
( Hockett, J.A. (2009) Curriculum for Highly Able Learners That Conforms to General Education and Gifted Education Quality Indicators. Journal of Education for the Gifted. Vol. 32, No. 3, p. 394-440)
High-quality curriculum for gifted learners uses a conceptual approach to organize or explore content that is discipline based and integrative.
High-quality curriculum for gifted learners pursues advanced levels of understanding beyond the general education curriculum through abstraction, depth, breadth, and complexity.
High-quality curriculum for gifted learners asks students to use processes and materials that approximate those of an expert, disciplinarian, or practicing professional.
High-quality curriculum for gifted learners emphasizes problems, products, and performances that are true to life, and outcomes that are transformational.
High-quality curriculum for gifted learners is flexible enough to accommodate self-directed learning fueled by student interests, adjustments for pacing, and variety.
COMPETENCY I
Examine data to describe the most important basic features of a data set.
Enabling Objectives:
Given a set of data, identify each variable as categorical or quantitative.
Make a histogram from a set of observations by choosing classes of equal widths, finding the class counts, and drawing the histogram.
Make a stemplot of the distribution of a small set of observations.
Describe the overall pattern of a distribution, including giving numerical measure of center and spread, describing the shape of the distribution, and recognizing outliers.
Make a timeplot of data and recognize strong trends and patterns.
Calculate measures of central tendency, including the mean, median, and mode of a set of observations.
Give the five number summary of a set of data and draw a boxplot.
Calculate the standard deviation for a set of observations.
Explain the important features of a density curve.
Know that the area under a density curve represents proportions of all observations.
Approximate the median and mean on a density curve.
Understand why some density curves are skewed.
Recognize the shape of a normal curve and estimate the mean and standard deviation of this curve.
Use the 68-95-99.7 rule and symmetry to describe the location of specific observations in a normal distribution.
Given a variable that has the normal distribution with a stated mean and standard deviation, find a value given a proportion.
COMPENTENCY II
Examine relationships for analysis of two or more variables.
Enabling Objectives:
Make a scatterplot for two quantitative variables.
Add a categorical variable to a scatterplot.
Recognize positive or negative association, linear patterns, and outliers in scatterplots.
Compute the correlation coefficient for small sets of observations.
Understand the basic properties of correlation.
Calculate the least-squares regression line for a set of data.
Use the least-squares regression line to extrapolate and predict values.
Determine how much of the variation of one variable can be accounted for by the straight-line relationship with another variable.
Recognize the possible influence of outliers on the least-squares regression line of a data set.
Calculate the residuals of a data set and plot them. Be able to recognize unusual patterns.
Understand that even a strong correlation does not imply a cause-and-effect relationship.
COMPENTENCY III
Design samples and experiments for producing data.
Enabling Objectives:
Identify the population in a sampling situation.
Recognize bias in certain sampling methods.
Use a table of random digits to select a random sample or a stratified random sample from a population or to carry out the random assignment of subjects to groups in a completely randomized experiment.
Recognize possible sources of error in a sample survey.
Determine whether a study is an observational study or an experiment.
Recognize possible sources of bias in an observational study or experiment.
Identify the components of an experimental design and outline the design of a completely randomized experiment.
Understand the placebo effect and recognize when the double-blind technique should be used.
Explain why a randomized comparative experiment can give good evidence for cause-and-effect relationships.
COMPENTENCY IV
Use probability and sampling distributions to draw conclusions about the population or process from which data come.
Enabling Objectives:
Identify parameters and statistics in a sample or experiment.
Interpret differences which may result from repeated trials of an experiment.
Describe the bias of a statistic in terms of the mean and spread of its sampling distribution.
Understand that variability of a statistic is controlled by the size of the sample.
Understand basic terminology associated with probability.
Interpret the sampling distribution of a statistic as describing the probabilities of its possible values.
Find the mean and standard deviation of a sample proportion from a simple random sample of a size n from a population having population proportion p.
Use the normal approximation to calculate probabilities which involve the sampling proportion.
Find the mean and standard deviation of a population having a binomial distribution.
Find the mean and standard deviation of a sample mean from a simple random sample when the mean and standard deviation of the population are known.
Use the central limit theorem to understand that the sampling distribution of the sample means of a population has approximately a normal distribution when the sample is large.
Use the law of large numbers to show that the actual observed outcome mean of a large number of observations must approach the population mean.
COMPENTENCY V
Draw conclusions about a population on the basis of sample data and use probability to indicate the reliability of conclusions.
Enabling Objectives:
Explain in nontechnical language what is meant by statements of confidence in statistic reports.
Calculate a confidence interval for the mean of a normal population with a known standard deviation.
Understand how the margin of error of a confidence interval changes with the sample size or the level of confidence.
Find the sample size required to obtain a confidence interval of specified margin of error when the confidence interval or other information is given.
State the null and alternative hypotheses in a testing situation when the parameter in question is the population mean.
Interpret the meaning of a p-value when you are given the numerical value of p for a test.
Calculate the z statistic and p-value for both one-sided and two-sided tests about the mean of a normal population.
Assess statistical significance at standard alpha levels either by comparing p to the standard alpha level or by comparing z to standard normal critical values.
Recognize when it is appropriate to use the z-test.
COMPENTENCY VI
Use t-tests and confidence intervals for inference about the mean of a single population and for comparing the means of two populations.
Enabling Objectives:
Recognize from a study whether one-sample, matched pairs, or two-sample procedures are needed to make an inference about a mean or comparing two means.
Use the t procedure to obtain a confidence interval at a stated level of confidence for the mean of a population.
Carry out a t test for the hypothesis that a population mean has a specified value against either a one-sided or a two-sided alternative.
Recognize the influence of outliers, design of the study, or sample size on the use of t procedures.
Use the t procedure to obtain confidence intervals and to perform tests of significance for matched pairs data.
Give a confidence interval for the difference between two means using the two-sample t statistic.
Test the hypothesis that two populations have equal means against either a one-sided or two-sided alternative using the t-test.
COMPENTENCY V II
Use statistical inference to draw conclusions about one or more parameters of a population.
Enabling Objectives:
Calculate from sample counts the sample proportion or proportions that estimate the parameters of interest.
Use the z procedure to give a confidence interval for a population proportion.
Use the z statistic to carry out a test of significance for the hypothesis H0: p = p0 about a population proportion against either a one-sided or a two-sided alternative.
Use the two-sample z procedure to give a confidence interval for the difference p1 p2 between proportions in two populations based on independent samples from the populations.
Use a z statistic to test the hypothesis H0: p1 = p2 that proportions in two distinct populations are equal.
COMPENTENCY VIII
Use two-way tables and the chi-square test to examine relationships among several parameters.
Enabling Objectives:
Arrange data on successes and failures in several groups into a two-way table of counts of successes and failures in all groups.
Use percentages to describe the relationship between two categorical variables starting from the counts in a two-way table.
Use your calculator to perform a chi-square test and interpret the results.
Explain what null hypotheses the chi-square tests in a specific two-way table.
Determine what deviations from the null hypothesis are significant.
Calculate the expected count for any cell from the observed counts in a two-way table.
Calculate the component of the chi-square statistic for any cell in a two-way table, as well as the overall statistic.
Give the degrees of freedom of a chi-square statistic.
Use the chi-square critical values to approximate the p-value of a chi-square test.
COMPENTENCY IX
Use statistical inference in the regression setting to explain relationships between an explanatory variable and a response variable.
Enabling Objectives:
Make a scatterplot to show the relationship between an explanatory and a response variable.
Use statistical software to find the correlation and least-squares regression line for a set of data.
Recognize the regression setting of a straight-line relationship between an explanatory variable and a response variable.
Determine the type of inference required in a particular regression setting.
Explain the meaning of the slope of a regression line.
<=KL\zxBCDHI`
NP01@A~+@A56op
""$"%"ʗʗʗh#OJPJQJh#5CJOJPJQJh#CJOJPJQJh#B*CJOJPJQJph333h#6CJOJPJQJh#5>*CJOJPJQJh#CJOJPJQJh#5CJOJPJQJ;<=KL\]yz
GHwx`ad@d]@ddd*<d]<ddddd$da$a
OP}xsnddd
&F
ld]l^`
&F
d]^`
&F
d]^`d
&F
d]^`d
&F
d]^`NO
x
&F
d^`$
0d]0^`a$$
&F
0d]0^`a$
&F
(d](^`d
&F
d^`dddr#$y?@m
&F
<d]<^`d
&F
d]^`
&F
d^`
&F
d]^`d
&F
d^`
&F
d]^`01@A~OKL
&F
Hd]H^`d
&F
d^`ddddd
&F
\d]\^`d0+@Ari
&F
d]^`d
&F
d^`ddddd
&F
d^`
&F
d]^`dij456op~ydd
&F
Td]T^`
&F
d]^`d
&F
(d](^`d
d^`
&F
d^`d
IK
&F
ld]l^`d
&F
d]^`
&F
d]^`d
&F
d^`ddd]d= > !!""$"%"|wrddd
&F
d]^`
&F
xd]x^`
&F
hd]h^`d
&F
d^`
&F
Dd]D^`d%""""######$$ %s
&F
Dd]D^`
&F
xd]x^`
&F
d^`
&F
d]^`d
&F
d]^`ddd]%""""e%f%&&&&J'_'`'**** +5+6+>,?,F,G,,,,,{-|---------/.D.E...}1~1112)2*23϶϶϶϶϶϶϶h#CJOJPJQJh#5CJOJPJQJh#CJOJPJQJh#OJPJQJh#6CJOJPJQJh#5CJOJPJQJ2 %d%e%f%%%|&&&&&J'_'}tod(d](ddd
&F
d^`
&F
d]^`d
&F
0d]0^`d
d^`
&F
d^`_'`'''k(l(((\)])))0*1*}
&F
Pd]P^`
&F
d]^`
&F
d]^`
&F
d]^`d
&F
d]^`d
1***** +5+6++++,,d
&F
d]^`d
&F
d^`
&F
0d]0^`ddddd
&F
d]^`,P-Q-----/.D.E....{d
d]^`
&F
d]^`dd]ddd
&F
d]^`d
&F
Td]T^`.D///#0z0{00)1}1~1112)2*2d d] ddd
&F
d^`d
&F
d^`
&F
@d]@^`*22222h333
&F
d^`
&F
Td]T^`
&F
d^`d
&F
d]^`/1h/ =!"#$%0/1h/ =!"#$%0/1h/ =!"#${%0/1h/ =!"#$%0/1h/ =!"#$%0s666666666vvvvvvvvv666666>6666666666666666666666666666666666666666666666666hH6666666666666666666666666666666666666666666666666666666666666666662 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@$OJPJQJ^J_HmH nH sH tH 8`8Normal_HmH sH tH DA D Default Paragraph Font6i60Table Normal(k ( 0No ListPK![Content_Types].xmlN0EH-J@%ǎǢ|ș$زULTB l,3;rØJB+$G]7O٭Vc:E3v@P~Ds |w<v
5e&+X1XbXXX%"3%ai%" %_'1*,.*23 !"#$&'()*+8@0(
B
S ?page1page2page3page4page5 5e&+ 5e&+yFEu|_Qb[T 'M# ͐
CfvZ%R3
.br
...............
#6++@+@Unknownm*Cx Times New RomanTimes New Roman PSCSymbolSymbol3.*Cx Arial7.@CalibriA$BCambria Math hXX^%O^%O!0++3HP $P62!xxMatthew R. BrowningMatthew R. BrowningD
Oh+'0l
(4
@LT\dMatthew R. BrowningNormalMatthew R. Browning2Microsoft Office Word@@s@s^%՜.+,0hp|
O+Title
!"#$%&'()*+,./0123456789:;<=>?@ABCDFGHIJKLNOPQRSTWRoot Entry F0{sY1Table-D.WordDocumentXSummaryInformation(EDocumentSummaryInformation8MCompObjr
F Microsoft Word 97-2003 Document
MSWordDocWord.Document.89q