## Course Content and Outcomes Guides (CCOG)

### CCOG for STAT 243 Summer 2024

Course Number:
STAT 243
Course Title:
Elementary Statistics I (MTH/STAT243=STAT243Z)
Credit Hours:
4
Lecture Hours:
30
Lecture/Lab Hours:
0
Lab Hours:
30

#### Course Description

Focuses on the interpretation and communication of statistical concepts. Introduces exploratory data analysis, descriptive statistics, sampling methods and distributions, point and interval estimates, hypothesis tests for means and proportions, and elements of probability and correlation. Uses technology when appropriate. This course is part of Oregon Common Course Numbering. MTH 243, STAT 243, and STAT 243Z are equivalent. The PCC Mathematics Department recommends that students take MTH courses in consecutive terms. Prerequisites: MTH 95 or MTH 98 or higher, and (WR 115 and RD 115) or IRW 115 or equivalent placement. Audit available.

This is the first term of a two-term sequence that is intended to provide an introduction to statistics in a data-based setting.

#### Intended Outcomes for the course

Upon completion of this course students should be able to:

1. Critically read, interpret, report, and communicate the results of a statistical study along with evaluating assumptions, potential for bias, scope, and limitations of statistical inference.

2. Produce and interpret summaries of numerical and categorical data as well as appropriate graphical and/or tabular representations.

3. Use the distribution of sample statistics to quantify uncertainty and apply the basic concepts of probability into statistical arguments.

4. Identify, conduct, and interpret appropriate parametric hypothesis tests.

5. Assess relationships in quantitative bivariate data.

#### Quantitative Reasoning

Students completing an associate degree at Portland Community College will be able to analyze questions or problems that impact the community and/or environment using quantitative information.

#### General education philosophy statement

Mathematics and Statistics courses help students gain tools to analyze and solve problems using numerical and abstract reasoning. Students will develop their abilities to reason quantitatively by working with numbers, operations, and relations and to reason qualitatively by analyzing patterns and making generalizations.

#### Course Activities and Design

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.

#### Outcome Assessment Strategies

Assessments worth at least 40% of the course grade will include both:

1. An individual, proctored, closed book examination
2. Either a second, individual, proctored, closed book examination OR a project culminating in a final product (ex. oral report, written report, video presentation, poster, slideshow, etc.)

Additionally, at least two of the following numbered measures:

1. Exams and/or quizzes (group or individual)
2. Projects
4. Online homework
5. Group or individual activities
6. Lab reports
7. Portfolios

Optional additional assessment strategies may include, but are not limited to

1. Individual student conferences
2. Discussions
3. Participation

#### 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

If time permits, the instructor may supplement the core course content with one or more of the following optional topics:

1. Experimental design
2. Linear Regression and the coefficient of determination (r2)
3. Theoretical probability topics and models (Venn Diagrams, Trees, etc.)
4. Discrete random variables and probability distributions
5. Expected value and standard deviation of discrete random variables
6. Bootstrapping
7. Plus-Four Method (for Confidence Intervals for a Proportion)
8. Simulation based methods to conduct tests of two proportions
9. Simulation based methods to conduct tests of two means