Portland Community College | Portland, Oregon

This is the first term of a two-term sequence (MTH 243 and 244) that is intended to provide an introduction to statistics in a data-based setting.

Upon successful completion students should be able to:

1. Analyze data and graphs in real world scenarios to recognize what probability and statistics are appropriate, formulate problems about the scenarios, creatively model these scenarios (using technology, if appropriate) in order to solve the problems using multiple approaches, then judge if the results are reasonable and clearly interpret the results via written or oral communication.
2. Appreciate probability and statistics concepts that are encountered in the real world, understand and be able to communicate the underlying mathematics involved to help another person gain insight into the situation.
3. Work with probability and statistics in various situations and use correct mathematical terminology, notation, and symbolic processes in order to be prepared for future coursework and to continue a course of study in their major field that requires the use of and an understanding of the concepts of probability and statistics.
4. Read a peer reviewed journal article and understand the meaning and logical implications behind the statistical processes of a confidence interval and a significance test.

All activities will follow the premise that formal definitions and procedures evolve from the investigation of practical problems. Concepts will be introduced using lecture, group activities, calculator programs, and/or computer laboratory explorations. Students will communicate their results orally and in writing.

Assessment must include:

1. At least two in-class or proctored examinations and
2. At least two of the following additional measures:
   1. take-home examinations.
   2. graded homework / worksheets.
   3. quizzes.
   4. writing assignments.
   5. group / individual projects.
   6. in-class activities.
   7. attendance.

1. Introduction
   The instructional goal is to explore how an understanding of statistics is beneficial to jobs in business, industry, government, medicine, and other fields.
   1. Describe and discuss descriptive and inferential statistics.
   2. Identify and describe common statistical terminology:
      1. population.
      2. sample.
      3. variable.
      4. statistical inference.

2. Describing Sets of Data
   The instructional goal is to explore, analyze, and describe a set of data using graphical and numerical methods.

   1. Identify qualitative and quantitative data.

   2. Construct bar charts.

   3. Interpret pie charts and bar charts.

   4. Construct frequency and relative frequency distributions.

   5. Construct frequency and relative frequency histograms.

   6. Construct a stem-and-leaf display.

   7. Construct a dotplot.

   8. Describe the shape of a distribution as symmetric, skewed left, or skewed right.

   9. Calculate and interpret the numerical measures of central tendency:

      1. mean.

      2. median.

      3. mode.

   10. Calculate and interpret the numerical measures of dispersion:

       1. range.

       2. inter-quartile range.

       3. variance.

       4. standard deviation.

   11. Interpret the meaning of the standard deviation using the Empirical Rule and/or Chebyshev’s Rule.

   12. Calculate and interpret measures of relative standing:

       1. percentile ranking.

       2. z -scores.

   13. Construct a modified boxplot.

   14. Look for relationships between two variables:
       1. Identify response and explanatory variables.
       2. Construct a scatterplot.

       3. Determine whether the two variables have a positive or negative association.

       4. Calculate and interpret the correlation coefficient,  r , and the coefficient of determination,  r2 .

       5. Calculate and interpret the least-squares regression line.

       6. Predict values of the dependent variable using the least-squares regression line.

       7. Discuss cautions about regression and correlation including:

          1. residuals.

          2. lurking variables.

          3. causation.

   15. Using technology,

       1. input and edit data.

       2. draw dotplots, histograms, boxplots, scatterplots, and residual plots.

       3. calculate one-variable summary statistics.

3. Producing Data
   The instructional goal is to explore the design of statistical samples and experiments.

   1. Identify the elements of experiments and observational studies including:

      1. experimental units.

      2. factors.

      3. placebo.

      4. bias.

      5. randomization.

   2. Identify the differences between experiments and observational studies.

   3. Identify sample designs including:

      1. voluntary response sample.

      2. convenience sample.

      3. simple random sample.

      4. stratified sample.

      5. multistage sample.

      6. systematic sample.

      7. cluster sample.

   4. Using technology or a table of random numbers select a simple random sample.

4. Elementary Probability
   The instructional goal is to explore the concepts of probability.

   1. Identify and describe standard probability terms:

      1. experiment.

      2. simple event (aka outcome).

      3. sample space.

      4. disjoint events.

      5. independent events.

      6. complementary events.

   2. Calculate and interpret marginal, joint, and conditional probabilities.

   3. Calculate and interpret probabilities using:

      1. Venn diagrams

      2. contingency tables.

      3. tree diagrams.

      4. additive rule.

      5. multiplicative rule.

   4. Calculate probabilities using Bayes’ Theorem.

5. Random Variables and Probability Distributions
   The instructional goal is to explore and analyze various random variables and probability distributions.

   1. Identify and describe terminology:

      1. random variable.

      2. probability distribution.

      3. expected value.

      4. variance and standard deviation.

      5. probability density function.

   2. Identify a random variable as discrete or continuous.

   3. Explore the binomial discrete probability distribution.

   4. Explore the normal continuous probability distribution.

   5. Approximate a binomial probability using a normal distribution.

   6. Using technology, input a probability density function and its appropriate parameters.

      1. Compute and interpret the probability that a discrete random variable is equal to a specified value.

      2. Compute and interpret the probability that a discrete random variable lies within an interval of values.

      3. Compute and interpret the probability that a continuous random variable lies within an interval of values.

   7. Using technology, simulate probability distributions by generating random data.

      1. Binomial.

      2. Normal.

   8. Compute and interpret the mean and standard deviation of

      1. a discrete random variable.

      2. a linear transformation of a random variable.

      3. the sum or difference of two independent random variables.

6. Sampling Distributions
   The instructional goal is to explore and analyze sampling distributions.

   1. Identify and describe terminology:

      1. parameter.

      2. statistic.

      3. point estimator.

      4. biased vs. unbiased.

   2. Calculate and interpret a sample mean and its standard deviation.

   3. Explore the distribution of the means of samples drawn from a population.

   4. Identify the properties of sampling distributions.

   5. Explore the Central Limit Theorem.

   6. Solve probability problems involving the standardized sample mean.

7. Estimation
   The instructional goal is to estimate a population parameter by calculating a confidence interval.

   1. Identify and describe terminology:

      1. confidence coefficient (aka critical  z -score).

      2. confidence level.

   2. Calculate and interpret a large-sample estimation of a population mean or proportion.

   3. Calculate a sample size to attain a desired margin of error and confidence level.

8. Significance Testing
   The instructional goal is to understand the logic, formal structure, appropriate use, and proper interpretation of significance testing.

   1. Identify and describe terminology:

      1. Null hypothesis (as an equation)

      2. Alternative hypothesis (one-sided and/or two-sided)

      3. Significance level ( \(\alpha\)-value)

      4. P -value

      5. Statistical significance

   2. Performance and interpretation:

      1. Specify an appropriate parameter of interest

      2. Identify/produce data, and properly set up a basic significance test

      3. Be able to compute a  P -value:

         1. Using a single (context-specific) significance test software function and/or

         2. Using a calculated test statistic and a software Cdf function, and/or

         3. Using a normal distribution table.

      4. Assess results for statistical significance against a predetermined significance level

      5. Distinguish between statistical vs. practical significance

   3. Compare the information a confidence interval provides versus a significance test.

   4. Verify required conditions for the test of significance.

If and only if time permits, the instructor may supplement the core course content with one or more of the following topics.

1. Counting Principles
   The instructional goal is to explore the counting principles.
   1. Calculate and interpret the number of simple events using the multiplication rule.
   2. Calculate and interpret the number of simple events using the partitions rule.
   3. Calculate and interpret the number of simple events using the permutations rule.
   4. Calculate and interpret the number of simple events using the combinations rule.
2. Additional Random Variables and Probability Distributions
   The instructional goal is to explore additional probability distributions.
   1. Explore discrete probability distributions:
      1. Geometric.
      2.  Poisson.
      3. Hypergeometric.
   2. Explore continuous probability distributions:
      1. Uniform.
      2. Exponential.