Overview
This lecture introduces Chapter Nine, which shifts focus from categorical data and proportions to numerical data and means, revisiting key concepts like sampling distributions, Central Limit Theorem, confidence intervals, and hypothesis testing.
Review of Previous Chapters
- Previous chapters focused on categorical data, which are described with words, labels, or descriptors.
- Analysis centered on proportions, representing the fraction of successes in categorical data (e.g., proportion of red M&M's).
Introduction to Numerical Data
- Chapter Nine focuses on numerical data, which are quantities measured with numbers (e.g., running times).
- Numerical variables will be summarized using the mean (average), instead of proportion.
- The mean is calculated by summing all numerical values and dividing by the total number of values.
Core Concepts in Chapter Nine
- The chapter will revisit sampling distributions, the Central Limit Theorem, confidence intervals, and hypothesis testing in the context of means.
- A major theme is comparing similarities and differences between analyzing categorical (proportions) and numerical (means) data.
Key Terms & Definitions
- Categorical Data — data described by labels or categories (e.g., colors).
- Proportion — fraction of items in a category that are considered a success.
- Numerical Data — data described by numbers, representing quantities or measurements.
- Mean — the average value of a set of numerical data, found by dividing the sum by the count.
- Sampling Distribution — the distribution of a statistic (like mean or proportion) across many samples.
- Central Limit Theorem — states that the sampling distribution of the sample mean approaches normality as sample size increases.
Action Items / Next Steps
- Review the concepts of sampling distributions, confidence intervals, and hypothesis testing as they relate to proportions.
- Prepare to apply these concepts to numerical data (means) in upcoming lessons.