Course Outline and Assignment Guide

 Unit 1 – Exploratory Data Analysis

      Objectives:  The student will: 

           1.  a)  develop an understanding of categorical (qualitative) data.
                b)  manually construct and interpret pie charts and bar graphs.
                c)  use coding and a graphing calculator to graph and interpret bar graphs
                          (by modifying the histogram).

           2.  a)  understand numeric (quantitative) data and manually construct & interpret a stemplot.
                b)  learn to create lists and then create and interpret histograms with the graphing calculator.

           3.  a)  further develop a knowledge of the list features in a graphing calculator.
                b)  use the connected dot plot feature of a calculator to graph and interpret ogives.

           4.  use a graphing calculator to construct and interpret time plots.

           5.  a)  develop a rudimentary understanding of center, shape and spread in interpreting data.
                b)  understand the difference of resistant (Median) and non-resistant (Mean) measures of center.

           6.  a)  develop a rudimentary understanding of spread by calculating 5-number summary manually.
                b)  use a graphing calculator to produce the 5-number summary.
                c)  interpret data sets by evaluating 5-number summary including the ability to identify outliers.
                d)  use the graphing calculator to construct box-whisker plots and modified boxplots .

           7.  a)  use a small data set to develop an understanding of how the s.d. is produced.
                b)  enter a data set into a  list and use 1-Variable Statistics to calculate the standard deviation.

           8.  a)  explore and describe the changes that occur to the center, shape, and spread when a data set adds a
                        constant value.
                b)  explore and describe the changes that occur to the center, shape, and spread when a data set is
                        multiplied by a constant.

Unit 2 – Normal Distributions

      Objectives:  The student will:  

           1.  a)  explore various histograms and correlate the shape to a density curve (normal distribution).
                b)  understand the Empirical Rule and use it to solve related problems .
                c)  understand the measure of spread in s.d. is a measure of distance from center of this distribution.

          2.  a)  re-center and re-shape (spread) a normal distribution to the standard normal curve ( µ = 0, σ = 1).
               b)  solve problems using the standard normal table (z-chart) in back of book.
               c)  solve problems using the normal distribution in the graphing calculator.

          3.  a)  solve problems of inverse normal procedure using the table (z-chart) in back of book.
               b)  solve problems of inverse normal procedures using an inverse normal program in the calculator.

          4.  a)  continue to work on advanced problems of normal distributions.
               b)  use the normal quantile plot in the graphing calculator to determine normality of data set.
               c)  establish when it is appropriate to use normality (normally distributed, no outliers, etc).
 

Unit 3 –  Bivariate Data & Relationship

     Objectives:  The student will:

          1.  a)  perform exploratory data analysis on bivariate data by entering into lists and graphing a scatterplot .
               b)  discuss key components of bivariate relationships:  direction,  shape, and strength.
               c)  understand the difference in causation and relation.

          2.  a)  manually calculate the correlation for a small data set to understand the contributing factors.
               b)  use the calculator to find the r-value for bivariate data linear relationships.

          3.  a)  calculate the least squares regression line from provided formulas.
               b)  use the graphing calculator to calculate the least squares regression line.
               c)  plot the least squares regression line on the scatterplot.

          4.  a)  understand the concepts of observed value, predicted value, and residuals.
               b)  use computer java script to manipulate a point and observe its effect on the regression line.
               c)  develop an intuitive understanding of influential points and outliers for bivariate data.

          5.  use the graphing calculator to compute the r-value of several data sets to understand a strong r does not
                      necessarily mean the data is linear.
 

Unit 4 –  More on Bivariate Data

     Objectives:  The student will:

          1.  a)  model exponential growth using a scatterplot on the graphing calculator.
               b)  transform exponential growth into a linear model by taking log y.
               c)  make prediction by converting linear model back to exponential growth.

          2.  a)  understand some of the limitations of modeling:  extrapolation, lurking variables, not-resistant.
               b)  construct residual plots to observe patterns that might indicate problems with the chosen model .
               c)  avoid assumptions of causation by understanding common response and confounding.       

          3.  a)  explore relationships in categorical data and model with bar graph and 2-way tables.
               b)  compute conditional distributions from row totals, column totals, and table totals.
               c)  examine examples of Simpson’s Paradox and write an explanation of how it occurs. 
 

Unit 5 –  Producing Data

     Objectives:  The student will:

          1.  a)  understand basic forms and differences of producing data: observational studies and experiments.
               b)  learn key terms: sample, census, simple random sampling, stratified random sampling etc.
               c)  discuss weaknesses of poor design and how to avoid undercoverage, non-response, bias, etc.

          2.  a)  use a table of random digits to select groups of individuals for a survey.
               b)  use the random number generator to select groups for an experiment.
               c)  discuss reasons why randomness must be created and not assumed.

          3.  a)  understand basic experimental design and its components.
               b)  describe an experiment, a blind experiment, and a double blind experiment.
               c)  describe block design, matched pairs design, and describe practical applications.

          6.  a)  fully describe how to set up a simulation to solve a problem.
               b)  use a table of random digits, a random number generator, or dice, to model a probability problem.
 

Unit 6 –  Probability

     Objectives:  The student will:

          1.  a)  describe random events by evaluating the definition.
               b)  compute basic probabilities to gain an understanding of predictability over long run.
               c)  describe events that have a probability of 1 and events with probability of 0.

          2.  a)  list the sample space and describe a probability model for an event.
               b)  construct a tree diagram to answer questions of probability.
               c)  develop an understanding of the multiplication principle and addition rule for disjoint events.
               d)  understand disjoint and independent and use multiplication rule when independent.

          4.  a)  use Venn diagrams to picture relationships among events.
               b)  find unions and intersections of multiple events.

          5.  a)  understand the idea of conditional probability.
               b)  find conditional probabilities from formula and tree diagrams.

          6.  construct tree diagrams to solve problems of several stages.

Unit 7 –  Random Variables

     Objectives:  The student will:

          1.  a)  understand and describe the characteristics of discrete random variables.
               b)  construct a probability model for a discrete random variable.
               c)  use a discrete random probability table to answer questions related to probability.

          2.  a)  understand and describe the characteristics of a continuous random variable.
               b)  construct a probability histogram and a density curve to describe probabilities.

          3.  a)  calculate the mean value (expected value) of random variables.
               b)  calculate the variance of a discrete random variable.

          4.  a)  use a coin to simulate and graphically comprehend the law of large numbers.
               b)  verbally describe the law of large numbers.

          5.  a)  learn and use the rules for means of random variables.
               b)  learn and use the rules for variances of random variables.
 

Unit 8 –  Binomial & Geometric Distributions

     Objectives:  The student will:

          1.  a)   identify the characteristics of a binomial distribution.
               b)  use a formula to answer questions of binomial distributions.
               c)  use a calculator program to answer questions of binomial distributions.

          2.  a)  determine when binomial distributions can be modeled by a normal distribution.
               b)  use normal distribution program to answer questions of binomial distribution.

          3.  a)  identify the characteristics of a geometric distribution.
               b)  use a formula to answer questions of geometric distributions.
               c)  use a calculator program to answer questions of geometric distributions.
 

Unit 9 –  Sampling Distributions

     Objectives:  The student will:

          1.  a)  identify basic terms and notation of sampling:  parameter/population,  statistic/sample.
               b)  observe patterns of sampling distributions by using a sampling program in calculator.
               c)  conclude that a statistic is unbiased if it is equal to the true parameter.

          2.  a)  understand that population size does not contribute to spread of sampling distribution.
               b)  chart the possibilities of sampling distribution in relation to high/low variability & high/low bias.

          3.  a)  use basic formulas to answer questions of sample proportions.
               b)  determine when to use the normal approximation for a sampling distribution of proportions.
               c)  use a calculator program to answer questions of sample proportions.

          4.  a)  use basic formulas of mean and standard deviation to answer questions of sample means.
               b)  use a calculator to show the sample proportion mean centers on the population proportion mean.

          5.  a)  use collected pennies to model the central limit theorem.
               b)  write a description of the properties discovered from modeling the C.L.T.
               c)  use a calculator program to observe C.L.T. as the sample size increases.
 

Unit 10 –  Introduction to Inference

     Objectives:  The student will:

          1.  a)  use thumbtacks to collect data and make a prediction about proportion of times point is up.
               b)  graph class results to see how each student’s prediction is slightly different.
               c)  observe the percentage of students who captured the true mean within their interval.
               d)  write a statement of confidence about thumbtacks using correct terminology.

          2.  a)  learn about confidence intervals for the mean and the requirements (z-intervals).
               b)  learn to correctly interpret and explain (verbally) a confidence interval.
               c)  use formula to construct a confidence interval for the mean.
               d)  use a graphing calculator to construct a confidence interval for the mean.

          3.  a)  identify the limitations of confidence intervals.
               b)  identify the requirements that must be met before making a statement of confidence

          4.  a)  learn about tests of significance for the mean and the requirements (z-test).
               b)  learn to correctly phrase a decision and conclusion.
               c)  use formula to construct a test of significance for the mean.
               d)  use a graphing calculator to test significance for the mean.

          5.  continue to practice confidence intervals and tests of significance manually and with calculator.

          6.  a)  explain why it is important to give the p-value and not just the conclusion.
               b)  explain validity of significance tests and requirements to produce validity.

          7.  a)  identify and calculate Type I errors.
               b)  describe a Type II error.
               c)  discuss power of the test.

Unit 11 –  Inference for Distributions

     Objectives:  The student will:

          1.  a)  understand the requirements of the t-distribution.
               b)  use formulas to construct a t-interval and conduct a t-test.
               c)  use graphing calculator to construct a t-interval and conduct a t-test.
               d)  observe the characteristics of the t-distribution and t-table as df increases.

          2.  a)  identify properties of matched pairs design and discuss when appropriate to use matched pairs.
               b)  use graphing calculator to answer questions of matched pairs design and make conclusions.
               c)  make conclusions from computer printout in relation to matched pairs design.

          3.  a)  use formulas of  two sample-t procedures to answer questions of comparison of means.
               b)  use graphing calculator to answer questions of two sample t-procedures.
               c)  make conclusions from computer printout in relation to two sample t-procedures.
 

Unit 12 –  Inference for Proportions

     Objectives:  The student will:

          1.  a)  identify when proportions may be modeled by normal distributions.
               b)  use formulas to construct an interval and perform a test for proportions.
               c)  use graphing calculator to construct an interval and perform a test for proportions.
               d)  determine sample sizes necessary to produced desired accuracy in proportions.

          2.  a)  use the 2-sample z procedure to give a C.I. for the difference of proportions.
               b) test hypothesis that two proportions are equal (from 2 populations)
               c) verify that the z-procedure is the correct procedure and meet the requirements.
 

Unit 13 –  Inference for Tables

     Objectives:  The student will:

          1.  a)  be able to compute the expected cell counts from formula and with calculator for goodness of fit.
               b)  compute the chi-square value and interpret it from a table in terms of probability.
               c)  test a hypothesis, reach a decision, and write a conclusion using goodness of fit procedures.
               d)  identify the requirements of the chi-square test of goodness of fit.

          2.  a)  be able to compute the expected cell counts from formula and with calculator for 2-way tables.
               b)  compute the chi-square value and interpret it from a table in terms of probability.
               c)  test a hypothesis, reach a decision, and write a conclusion using goodness of fit procedures.
               d)  identify the requirements of the chi-square test for two-way tables