Thursday Suggested HW: "Random Variables and Probability" Packet

• Here are the answers...
• 1.) A college student....
• Mean = $219
• St. Dev. = $9.868
• A random variable X...
• B
• 2.) A local radio station...
• a.) Mean = 156 min, St. Dev. = 7.5895 min
• b.) 0.000783 or 7.828E-4
• Ten percent of all Dynamite Mints....
• D
• A company shifts gift baskets...
• B
• Research indicates that the standard deviation...
• B
• The random variable x is normally distributed...
• D
• The SC Electric Company has bid on two electrical wiring jobs...
• C
• It is estimate that, at a certain university...
• a.) 0.00137
• b.) 0.2007
• c.) 0.61772
• A plumbing contractor...
• A
• A blind taste test will be conducted...
• B

Table of Tests/Intervals: The formulas are not provided; although we don't need to show these for a free response, we do need to know all this stuff--so one additional way to study is to copy all this information into your notes (if you copy it down you will retain it; if you just look at the pictures, you will not.) Then, go back through your notes and provide all of the missing formulas!

More Topics Related to Hypothesis Tests/Confidence Interval To Study:

• Interpret the meaning of the confidence level
• Know how changes in sample size and confidence level affect the margin of error and the width of an interval
• Know how changes in sample size affect the standard deviation/standard error
• Find the value of a point estimate (the sample statistic) given the interval
• Find the margin of error given the interval
• Calculate margin of error given the sample data
• Use a confidence interval to test hypotheses
• Use a 2 sample confidence interval to determine if it shows evidence of a significant difference
• Define Type I and Type II errors, and be able to identify consequences of each (if info about this is in the context)
• Interpret p-value in context
• Interpret the meaning of power in context
• Know how power is calculated
• Know how to decrease power
• Know that alpha and beta are the probabilities of Type I/Type II errors, and how changing alpha affects beta
• Let me know if I left anything off this list!

Topics to Study: Here's  a list of the topics we've learned throughout the year (other than all the inference stuff above)

• This is a brief/general overview--not necessarily every detail we need to know

AP Exam Review: Topic List

1. 1. Creating/Describing Distributions
   a.      Creating a histogram—by hand and on calculator
   b.      Creating a boxplot—*by hand* and on calculator
                                                       i.     Determining outliers using fences
   c.      Creating/Reading/Describing…
                                                       i.     Dotplot
                                                      ii.     Stem and Leaf plot
                                                     iii.     Cumulative Frequency Histogram
   d.      Describing a distribution
                                                       i.     Shape: skewed vs. symmetric
                                                      ii.     Center: mean vs. median
                                                     iii.     Spread: standard deviation vs. IQR (and can also use range)
                                                     iv.     Note gaps
                                                      v.     Note outliers
   e.      Adding a constant to a data set: affects center, but not spread
   f.       Multiplying by a constant to a data set: affects both center and spread
   g.      The Normal Model
                                                       i.     What is a z-score?
                                                      ii.     Calculating z-scores
                                                     iii.     Using z-scores to find probability
   1.      Normalcdf(lower bound, upper bound, mean, standard deviation)
   2.      Using z-table (not necessary if you can use normalcdf)
   3.      68/95/99.7 rule
   2.      Linear Regression
   a.      Interpret slope
   b.      Interpret y-intercept
   c.      Reading computer output—identify slope, y-int, standard deviation of x, standard deviation of residuals
   d.      Interpreting the Coefficient of Determination (R^2)
   e.      Describing a scatterplot:
                                                       i.     Shape, direction, strength (r)
   f.       Examining/creating a residual plot
                                                       i.     Overestimate: residual is (-); Underestimate: residual is (+)
   g.      Finding LSRL with calculator
                                                       i.     STATàCALCà(8)LinReg(a+bx) L1, L2, Y1
   1.      Used to find r, R^2
   2.      Also need to do this before you can look at a residual plot
   h.      Outliers, Influence, and Leverage
   i.       Lurking Variables
   3.      Sample Surveys
   a.      Understanding randomness
                                                       i.     Describing randomization processes—using random number generator, cards, names from a hat, etc.
                                                      ii.     Using random number tables
   b.      Sampling Methods
                                                       i.     SRS
                                                      ii.     Stratified
                                                     iii.     Cluster
                                                     iv.     Convenience
                                                      v.     Systematic
   c.      Bias: over or under representing a specific group in the population
                                                       i.     Response Bias
                                                      ii.     Nonresponse Bias—people have the choice, and some do not respond, leaving out part of the population
                                                     iii.     Voluntary Response Bias
                                                     iv.     Undercoverage—your design misses part of the population
   4.      Experimental Design
   a.      Writing experimental designs/procedures
                                                       i.     Response Variable
                                                      ii.     Factors, levels, treatments
                                                     iii.     Control, Randomization, Replication—and don’t forget to comment on comparison!
   b.      Blocking: create homogenous groups to allow for better comparison
   c.      Confounding Variables
   d.      Single vs. Double Blind
   5.      Observational Studies
   a.      Retrospective vs. Prospective
   b.      Matching (same as blocking, but for observational studies)
   6.      Probability
   a.      Venn Diagrams
   b.      Conditional Probability
                                                       i.     Tree Diagrams
   c.      Independence Formula: P(B/A) = P(A)
   d.      Expected Value and Variance
                                                       i.     Remember, we cannot add standard deviations but we can ALWAYS ADD VARIANCES
                                                      ii.     Using a Normal model after finding a new E(X), variance
   e.      “And, Or, Not, Given”
   f.       Binomial Probability Distribution
                                                       i.     Binomialpdf( à Used when given a specific sample size and one specific number of successes
                                                      ii.     Binomialcdf( à Cumulative; used when given a specific sample size and multiple numbers of successes
   g.      Geometric Probability Distribution
                                                       i.     Used to calculate the “first” (Hint: if you simply use the ideas of “and,or” you won’t really need to use a geometric distribution)
   h.      Mutually Exclusive/Disjoint VS. Independent
   7.      Statistical Inference
   a.      See statistical inference chart