Course Overview

This syllabus outlines the structure, content, and expectations for the course Introduction to Statistics (MTH213) at Owens Community College. The course provides foundational knowledge in both descriptive and inferential statistics, emphasizing critical thinking and practical application of statistical methods.

Course Topics and Structure

1. Introduction to Statistics

This section introduces the field of statistics, focusing on the collection, classification, and analysis of data. Students learn about different types of data and the importance of experimental design in statistical studies.

• Key Terms: Population, sample, variable, data, parameter, statistic

• Data Collection Methods: Surveys, experiments, observational studies

• Experimental Design Principles: Randomization, replication, control

• Example: Designing a survey to estimate average student study hours per week.

2. Descriptive Statistics

Descriptive statistics involve summarizing and organizing data using tables, graphs, and numerical measures. This topic covers frequency distributions, graphical displays, and measures of central tendency and dispersion.

• Tables and Graphs: Frequency tables, histograms, bar graphs, pie charts

• Measures of Central Tendency: Mean, median, mode

• Measures of Variation: Range, variance, standard deviation

• Measures of Position: Percentiles, quartiles, z-scores

• Example: Creating a histogram to display exam scores.

3. Probability

This section introduces the basic concepts of probability, including rules for calculating probabilities and the use of probability in statistical inference.

• Basic Probability Concepts: Experiment, outcome, event, sample space

• Rules of Probability: Addition rule for disjoint events, multiplication rule for independent events

• Conditional Probability: Probability of an event given another event has occurred

• Counting Techniques: Permutations and combinations

• Example: Calculating the probability of drawing two aces from a deck of cards.

4. Discrete and Binomial Probability Distributions

Students learn about discrete random variables, probability distributions, and the binomial distribution, which models the number of successes in a fixed number of independent trials.

• Discrete Random Variables: Variables that take on countable values

• Probability Distribution: Lists each possible value and its probability

• Binomial Distribution:

• Example: Probability of getting 3 heads in 5 coin tosses.

5. Normal Distribution and Continuous Random Variables

This topic covers the properties of the normal distribution, standard normal distribution, and the use of z-scores to find probabilities and values.

• Normal Distribution: Bell-shaped, symmetric distribution

• Standard Normal Distribution: Mean 0, standard deviation 1

• Z-Score Formula:

• Example: Finding the probability that a value is greater than a given z-score.

6. Sampling Distributions and the Central Limit Theorem

Students are introduced to the concept of sampling distributions and the Central Limit Theorem, which describes the distribution of sample means.

• Sampling Distribution: Probability distribution of a statistic based on a random sample

• Central Limit Theorem: For large samples, the sampling distribution of the mean is approximately normal

• Formula for Standard Error:

• Example: Simulating sample means from a population to observe the Central Limit Theorem.

7. Confidence Intervals

This section explains how to estimate population parameters using confidence intervals for means and proportions, and how to interpret the confidence level and margin of error.

• Confidence Interval for Mean (σ unknown):

• Confidence Interval for Proportion:

• Margin of Error: Depends on sample size and confidence level

• Example: Calculating a 95% confidence interval for the average height of students.

8. Hypothesis Testing

Students learn the logic and framework of hypothesis testing for means and proportions, including formulating hypotheses, calculating test statistics, and interpreting p-values.

• Null and Alternative Hypotheses: and

• Test Statistic: (for known σ)

• P-value: Probability of observing a test statistic as extreme as, or more extreme than, the observed value under

• Type I and II Errors: False positive and false negative conclusions

• Example: Testing whether a new teaching method improves test scores.

9. Two-Sample Inference

This topic covers interval estimation and hypothesis testing for differences between two means or proportions, as well as the chi-square test for independence.

• Two-Sample t-Test: Comparing means from two independent groups

• Chi-Square Test: Testing for independence in categorical data

• Example: Comparing average exam scores between two classes.

10. Correlation and Regression

Students explore relationships between two quantitative variables using correlation coefficients and least squares regression lines.

• Correlation Coefficient (r): Measures strength and direction of linear relationship

• Least Squares Regression Line:

• Interpretation: Caution in inferring causation from correlation

• Example: Analyzing the relationship between study time and exam scores.

11. Chi-Square Tests and ANOVA

This section introduces the chi-square test for goodness of fit and independence, as well as the basics of analysis of variance (ANOVA) for comparing means across multiple groups.

• Chi-Square Test Statistic:

• ANOVA: Tests for differences among group means

• Example: Testing whether dice are fair (goodness of fit).

Course Requirements and Evaluation

• Assignments: 7 homework assignments, 7 quizzes, midterm exam, and final exam

• Grading Scale:

  • A: 90% - 100%

  • B: 80% - 89.99%

  • C: 70% - 79.99%

  • D: 60% - 69.99%

  • F: < 60%

• Technology: Access to MyLab Statistics, StatCrunch, and a webcam-equipped computer is required.

• Academic Integrity: Use of AI during quizzes and exams is prohibited. Academic dishonesty results in severe penalties.

Support and Policies

• Disability Accommodations: Contact the Disability Resource Center for support.

• Anti-Discrimination and Title IX: Policies strictly enforced; see college website for details.

• Technical Support: Contact the Owens Help Desk or Pearson Support for technical issues.

• Math Tutoring: Available on both campuses and online by appointment.

Course Calendar and Deadlines

The course follows a detailed weekly schedule, with specific chapters and assignments due each week. Students are responsible for keeping track of deadlines and completing all assignments, quizzes, and exams within the designated windows.

Table: Major Course Topics and Corresponding Weeks

Additional info:

• This syllabus provides a comprehensive overview of the course structure and expectations. Students are encouraged to use the provided resources and seek support as needed to succeed in the course.