Portland Community College | Portland, Oregon

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

• Apply statistical problem solving strategies in limited 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 (STAT 243) – (Taken from the STAT 243Z CCOG)

Course Content (Themes, Concepts, Issues and Skills)

1. Identify and describe common statistical terminology: descriptive statistics, inferential statistics, population, sample, variable, observational units, statistic, parameter, quantitative (numerical) data, qualitative (categorical) data, observational study, experiment 
2. Consider the quality and appropriateness of data collection methods
   1. Identify and describe common sampling methods: voluntary response, convenience sampling, simple random sampling, stratified sampling, systematic sampling, cluster sampling, multistage sampling
   2. Explore representativeness and the potential for bias
3. Analyze qualitative (categorical) data from one and two variables
   1. Compute statistics: proportion
   2. Construct and interpret: (relative) frequency table, two way tables, bar graphs
   3. Use two way tables to introduce probability, including joint, marginal, and conditional probabilities
   4. Use conditional probability to check for independence
4. Analyze quantitative (numerical) data from a single variable
   1. Compute statistics using technology: mean, median, standard deviation, 5-number summary, IQR
   2. Construct and interpret: (relative) frequency table, dotplot, histogram, modified boxplot
   3. Describe the shape of a distribution and identify outliers (if any)
   4. Determine relative standing using z-scores
   5. Interpret the results of statistical analysis in context 
   6. Use illustrations and summaries to compare and contrast distributions
5. Explore relationships between two quantitative (numerical) variables 
   1. Identify and describe: explanatory variable, response variable, correlation, residual
   2. Construct a scatterplot using technology and assess the linear/non linear relationship between variables
   3. Use technology to determine the correlation coefficient and interpret its meaning in context
   4. Use technology to determine the line of best fit (least squares regression line) and use it to make predictions
   5. Discuss cautions and limitations: lurking and confounding variables, correlation versus causation, extrapolation
6. Explore the properties of normal distributions
   1. Identify and describe: normal distribution, standard normal distribution, parameters
   2. Use technology to perform calculations from a normal distribution
   3. Use technology to determine the critical value from a standard normal distribution
7. Explore and analyze sampling distributions
   1. Identify and describe: parameter, statistic, random variable, sampling variability, binomial, Central Limit Theorem 
   2. Perform simulations to investigate sampling distributions (counts, proportions, means) and perform probability calculations
   3. Determine when the Central Limit Theorem applies to a distribution
   4. Use technology to perform probability calculations for sample means and sample proportions based on the Central Limit Theorem 
   5. Describe how sample size, shape of the population, population mean and standard deviation impact the distribution of sample means 
8. Create and interpret confidence intervals 
   1. Identify and describe: level of confidence, margin of error, standard error, critical values, student’s t distribution
   2. Understand the construction and meaning of confidence intervals
   3. Determine point and interval estimates of the population mean and population proportion using theoretical and/or simulation based methods
   4. Interpret confidence intervals in context using correct units of measurement
   5. Describe the relationship between sample size, level of confidence, and margin of error in the construction of confidence intervals
   6. Given a specified confidence level, determine the minimum sample size required to attain a specified margin of error.
9. Conduct, and interpret hypothesis tests
   1. Identify and describe: null and alternative hypotheses, significance level, p-value, statistical significance, test statistic
   2. Understand the logic of hypothesis testing
   3. Identify the appropriate test based on variable type 
   4. Use theoretical and/or simulation based methods to conduct one and two tailed tests of a single mean
   5. Use theoretical and/or simulation based methods to conduct one and two tailed tests of a single proportion
   6. Interpret test conclusions in context
   7. Describe the potential for error in the decision making process 
   8. Distinguish the difference between statistical and practical significance
   9. Investigate the relationship between hypothesis tests and confidence intervals

Optional topics may include:

• Experimental design
• Linear Regression and the coefficient of determination (\(r^2\))
• Theoretical probability topics and models (Venn Diagrams, Trees, etc).
• Discrete random variables and probability distributions
• Expected value and standard deviation of discrete random variables
• Bootstrapping
• Plus-Four Method (for Confidence Intervals for a Proportion)
• Simulation based methods to conduct tests of two proportions
• Simulation based methods to conduct tests of two means

ALM ADDENDUM:

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

Specifically, the ALM course:

• supports students concurrently enrolled in MTH/STAT courses;

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

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