Portland Community College | Portland, Oregon

This class is not intended to be a study hall for students to work on MTH assignments. The time needs to be spent working on material designated by your ALM instructor. If a student is co-enrolled in a MTH class, then this may include targeted materials which are intended to support the concepts being taught in that MTH class. 

Upon completion of the course students should be able to:

• Perform appropriate statistical and/or mathematical computations for a variety of situations either by hand or using an approved technology in a wide variety of situations.

• Apply statistical problem solving strategies in multiple contexts.

• Address statistical problems with increased confidence.

• Demonstrate progression through learning objectives established between the student and instructor.

Instructors may employ the use of worksheets, textbooks, online software, mini-lectures, and/or group work.

Assessment shall include at least two of the following measures:

1. Active participation/effort

2. Personal program/portfolios

3. Individual student conference

4. Assignments

5. Pre/post evaluations

6. Tests/Quizzes

Items from the course content may be chosen as appropriate for each student and some students may even work on content from other ALM courses as deemed appropriate by the instructor.

Statistics I (MTH 243) – (Taken from the MTH 243 CCOG)

Course Content (Themes, Concepts, Issues and Skills)

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,  r^2 .

   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 Chebyshev'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.

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

ALM ADDENDUM:

The mission of the Math ALM is to promote student success in MTH courses by tailoring the coursework to meet individual student needs.  

Specifically, the ALM course:

• supports students concurrently enrolled in MTH courses;

• prepares students to take a MTH course the following term;

• allows students to work through the content of a MTH course over multiple terms;