## Lesson 8: Sampling Distributions and the Central Limit Theorem

September 19, 2024

Review:

- Exam 1 Review
- Census and Sampling
- Battleground State poll margin of error calculation
- Latest Polls (NYTimes)

Presentation:

**Samples and Surveys**- Toward Statistical Inference
- Population parameters
- Sample statistics
- Sampling distribution
- Bias and Variability
- to reduce bias, use random sampling
- to reduce variability, use larger sample sizes (p. 215)

**Video**: Samples and Surveys (Disc 3, Unit 17)

- Toward Statistical Inference

**The Sampling Distribution of a Sample Mean**- Take multiple Simple Random Samples, sample size = n, and calculate each sample mean
- “Sampling Distribution” is the distribution of sample means
**Standard deviation of sample means = s/√n**- Central Limit Theorem: Simple random samples of size n from
**any**population with mean μ and finite standard distribution σ. When n is large (typically ≥ 30), the sampling distribution of the sample mean is approximately**Normal**. **Video**: Sampling Distributions (Disc 3, Unit 22)

Activity:

- Read p. 335-344
- Complete problems 5.36, 5.37, 5.38 and 5.39