AP Statistics Semester Exam Review
Time and Date:  12:30-2:30 Friday, Jan 7
Location TBA

The semester exam will be similar in nature to the AP Statistica exam in that the multiple choice and the free response will carry equal weight.  You should review all of your tests and quizzes and use this list to direct your study for the exam.  Bring pencils with erasers, and your calculator.  Your calculator will be available for use during the entire exam.

These are the skills you should have acquired:

Chapter 1:  Exploring Data

Data

• Identify the individuals and variables in a set of data
• Identify each variable as categorical or quantitative.  Identify the units in which each quantitative variable is measured.

Dotplots and Histograms

• Make a dotplot that records dots for individual observations
• Make a histogram of the distribution of a quantitative variable when you are given counts for classes of equal width
• Make a histogram from a set of observations by choosing classes of equal widths, finding the class counts, and drawing the  histogram

Stemplots

• Make a stemplot of the distribution of a small set of observations
• Round leaves or split stems as needed to make an effective stemplot

Inspecting Distributions

• Look for the overall pattern and for major deviations from the pattern
• Describe the overall pattern by giving numerical measures of center and spread and a verbal description of shape
• Assess from a dotplot, stemplot, or histogram whether the shape of a distribution is roughly symmetric, distinctly skewed, or neither
• Decide which measures of center and spread are mote appropriate:  the mean and standard deviation (especially for symmetric distributions) or the five-number summary (especially for skewed distributions)
• Recognize outliers

Time Plots

• Make a time plot of data, with the time of each observation on the horizontal axis and the value of the observed variable on the vertical axis
• Recognize strong trends or other patterns in a time plot

Measuring Center

• Calculate the mean (x bar) of a set of observations using a calculator
• Determine the median (M) of a set of observations
• Understand that the median is less affected by extreme observations than the mean
• Recognize that the skewness in a distribution moves the mean away from the median toward the long tail

Measuring Spread

• Calculate the quartiles Q1 and Q3 and the IQR for a set of observations
• Give the five-number summary and draw a boxplot; assess symmetry and skewness from a boxplot
• Calculate the standard deviation (s) for a set of observations using a calculator
• Know the basic properties of s:  s is always greater than or equal to 0, s = 0 only when all observations are identical and increases as the spread increases; s has the same units as the original measurements; s is pulled strongly by outliers or skewness in the observations

Chapter 2:  The Normal Distributions
Density Curves

• Know that areas under a density curve represent proportions of all observations and that the total area under a density curve is 1
• Approximately locate the median (equal areas point) and the mean (balance point) on a density curve
• Know that the mean and median both lie at the center of a symmetric density curve and that the mean moves farther toward the long tail of a skewed curve.

Normal Distributions

• Recognize the shape of  normal curves and be able to estimate both the mean and standard deviation from such a curve
• Use the 68-95-99.7 rule and symmetry to state what percent of the observations from a normal distribution fall between two points when both points lie at the mean or one, two ,or three standard deviations on either side of the mean
• Given that a variable has the normal distribution with a stated mean (mu,µ) and standard deviation (sigma), calculate the proportion of values above a stated number, below a stated number, or between two stated numbers
• Given that a variable has the normal distributions with a stated mean and standard deviation, calculate the point having a stated proportion of all values above it
• Also calculate the point having a stated proportion of all values below it

Assessing Normality

• Plot a histogram, stemplot, and/or boxplot to determine if a distribution is approximately normal
• Construct and interpret normal probability plots

Chapter 3:  Examining Relationships
Data

• Recognize whether each variable is quantitative or categorical
• Identify the explanatory and response variables in situations where one variable explains or influences the other

Scatterplots

• Make a scatterplot for two quantitative variables, placing the explanatory variable (if any) on the horizontal axis
• Add a categorical variable to the scatterplot by using a different plotting symbol
• Recognize positive or negative association, a linear pattern, and outliers in a scatterplot

Correlation

• Compute the correlation coefficient, r, for small sets of observations using the formula
• Know the basic properties or correlation: r measures the strength and direction of linear relationships only; -1 < r < 1 always; r = ± 1 only for perfect straight-line relationships; r moves away from 0 toward ± 1 as the linear relationship gets stronger

Straight Lines

• Explain what the slope, b, and the intercept, a, mean in the equation y = a + bx
• Draw a graph of the straight line when you are given its equation

Regression

• Calculate the least squares regression line of a response variable y on an explanatory variable x from data using a calculator
• Find the slope and the intercept of the least squares regression line from the means and standard deviations and correlation of x and y
• Use the regression line to predict y for a given x.  Recognize extrapolation and be award of its dangers
• Use r² to describe how much of the variation in one variable can be accounted for by a straight line relationship with another variable
• Recognize outliers and potentially influential observations from a scatterplot with the regression line drawn on it
• Calculate the residuals and plot them against explanatory variable x or against other variables.  Recognize unusual patterns

Chapter 4: More on Two-Variable Data
Modeling Non-Linear Data

• Recognize that when a variable is multiplied by a fixed number greater than 1 in each equal time period, exponential growth results; when the ratio is a positive number less than 1, exponential decay occurs
• Recognize that when one variable is proportional to a power of a second variable, the result is a power function
• In the case of both exponential growth and power function, perform a logarithmic transformation and obtain points that lie in a more linear pattern.  Then use least squares regression on the transformed points.  An inverse transformation then produces a curve that is a model for the original points
• Know that deviations from the overall pattern are most easily examined by fitting a line to the transformed points and plotting the residuals from this line against the explanatory variable (or fitted values.)

Interpreting Correlation and Regression

• Understand that both r and the least squares regression line can be strongly influenced by a few extreme observations
• Recognize possible lurking variables that may explain the observed association between two variables x and y
• Understand that even a strong correlation does not mean that there is a cause-and-effect relationship between x and y

Chapter 5: Producing Data
Sampling

• Identify the population in a sampling situation
• Recognize bias due to voluntary response samples and other inferior sampling methods
• Use a table of random digits to select a simple random sample (SRS) from a population
• Recognize the presence of undercoverage and nonresponse as sources of error in a sample survey.  Recognize the effect of the wording of questions on the responses.
• Use random digits to select a stratified random sample from a population when the strata are identified

Experiments

• Recognize whether a study is an observational study or an experiment
• Recognize bias due to confounding of explanatory variables with lurking variables in either an observational study or an experiment
• Identify the factors (explanatory variables), treatments, response variables, and experimental units or subjects in an experiment
• Outline the design of a completely randomized experiment using a diagram.  The diagram in a specific case should show the sizes of the groups, the specific treatments, and the response variable
• Use a table of random digits to carry out the random assignment of subjects to groups in a completely randomized experiment
• Recognize the placebo effect.  Recognize when the double-blind technique should be used
• Explain why a randomized comparative experiment can give good evidence for a cause-and-effect relationship

Simulations

• Recognize that many random phenomena can be investigated by means of a carefully designed simulation
• Use the steps to construct and run a simulation
• state the problem or describe the experiment
• state the assumptions (don't forget trials are independent of one another)
• assign digits to represent outcomes
• simulate many repetitions
• calculate relative frequencies and state your conclusions
• Use a random digit table, the TI-83, or a computer software package to conduct simulations

Chapter 6:  Probability:  The Study of Randomness
The Probability Model

• Describe the sample space of a random phenomenon.  For a finite number of outcomes, use the multiplication principle to determine the number of outcomes, and use counting techniques, Venn diagrams, and tree diagrams to determine simple probabilities.  For the continuous case, use geometric areas to find probabilities (areas under simple density curves) of events (intervals on the horizontal axis)
• Know the probability rules and be able to apply then to determine probabilities of defined events.  In particular, determine if a given assignment of probabilities is valid.
• Determine if two events are disjoint, complementary, independent, or dependent.  Find unions and intersections of two or more events
• Know the general addition rule for the union of two events, and how to apply it
• Define conditional probability and use the definition to find conditional probabilities of events
• Use the multiplication rule to find the joint probability of two events
• Construct tree diagrams to organize the use of the multiplication and addition rules to solve problems with several stages

Chapter 7:  Random Variables
Random Variables

• Recognize and define a discrete random variable, and construct a probability distribution table and probability histogram for the random variable
• Recognize and define a continuous random variable, and determine probabilities of events as areas under density curves
• Given a normal random variable, use the standard normal table or a TI-83 to find probabilities of events as areas under the standard normal curve

Means and Variances

• Calculate the mean and variance of a discrete random variable.  Find the expected payout in a raffle or similar game of chance
• Use simulation methods and the law of large numbers to approximate the mean of a distribution
• Use rules for means and rules for variances to solve problems involving sums and differences of random variables