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 completion of the course students should be able to:

1. Identify statistical results and terminology in politics, popular culture, and scientific studies and state their relevance.
2. Use statistical thinking to identify, answer and interpret meaningful questions.
3. Generate appropriate graphical and numerical summaries for various situations.
4. Describe and identify the role and importance of variability and randomness in statistics.
5. Use statistical models (single and multivariable) and statistical inference (hypothesis testing and confidence intervals) in a range of contextual settings and draw appropriate conclusions.
6. Use statistical software to analyze data, carry out inference and make conclusions.
7. Be prepared to continue a course of study in a major field that requires the use and understanding of the concepts and logical implications of probability and statistics.

1. Teach Statistical Thinking – Students should think of statistics as a problem solving and decision making process instead of a collection of formulas and methods.
2. Focus on Conceptual Understanding – Students should primarily apply concepts rather than rely on computations. Focus on depth of content, not breadth of topics.
3. Integrate Real data with context and purpose – Use data sets and or studies that are real and are relevant to student’s interests.
4. Foster Active Learning – Use group work that allows for discussion and predictions rather than step by step procedures. Have students do basic physical simulations before computer driven simulations.
5. Use Technology - Use technology and computer software to analyze and investigate larger data sets.

Assessment must include:

1. At least two in-class or proctored examinations. These exams must consist primarily of free response questions although a limited number of multiple choice and/or fill in the blank questions may be used where appropriate.
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.
      5. biased vs. unbiased
   3. Identify the elements of experiments and observational studies including:
      1. experimental units/
      2. factors
      3. placebo
      4. bias
      5. randomization
   4. Identify the differences between experiments and observational studies.
   5. 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.
   6. Using technology or a table of random numbers select a simple random sample.

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. standard deviation.

   11. Calculate and interpret measures of relative standing:

       1. percentile.

       2. z -scores.

   12. Interpret the meaning of the standard deviation using the Empirical Rule.

   13. Construct a modified boxplot.

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

   1. Create a two way table and investigate simple, joint, marginal and conditional probability.

   2. Identify and describe:

      1. experiments.

      2. event.

      3. sample spaces.

      4. disjoint events.

      5. tests for independence.

      6. complementary events.

4. 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 a discrete random variable.

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

   1. Identify and describe terminology:

      1. parameter.

      2. statistic.

      3. point estimator.

   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.

6. 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.

7. 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 a statement and 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

      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.

8. The instructional goal is to 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 using technology

   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

   8. Using technology,

      1. input and edit data.

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

      3. calculate one-variable summary statistics.

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

1. Calculate and interpret probabilities in using:

   1. Venn Diagrams

   2. tree diagrams.

   3. additive rule.

   4. multiplicative rule.

   5. calculate probabilities using Baye's Theorem.

2. Calculate and interpret the numerical measures of dispersion with variance.

3. Interpret the meaning of the standard deviation using Checyshev's Rule.

4. For Random Variables identify and describe variance.

5. For a linear transformation of a random variable:

   1. Find the sum or difference of two independent random variables

6. Approximate a binomial probability using a normal distribution.

7. Compute a P-value using a normal distribution table.

8. 1. Explore discrete probability distributions:
      1. Geometric.
      2.  Poisson.
      3. Hypergeometric.
   2. Explore continuous probability distributions:
      1. Uniform.
      2. Exponential.