Lesson 10: Sampling, Inference and the Central Limit Theorem
October 5, 2026
Review:
- Exam 2 results
Presentation:
- Census and Sampling
- Census = attempt to count entire population
- US Census every 10 years
- Most costly non-military federal government operation
- Sample = gather info from a portion of the population
- Sample Types
- Voluntary response sample
- Complete an optional survey
- Inherent bias
- Example: Survey Monkey or Google Forms
- Simple random sample
- select from a population
- each individual has equal chance of being selected
- Example: random selection of subset of enrolled students
- Stratified random sample
- divide population into groups or strata
- random sampling, equal chance of selection within each group
- Example: random selection within major (30% CIS, 35% Mgmt, 35% Econ)
- Voluntary response sample
- Sample Types
- Census = attempt to count entire population
- 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
- 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 (CLT)
- If you take simple random samples of size n from any population with mean μ and finite standard distribution σ. Then, when n is sufficiently large (typically ≥ 30), the sampling distribution of the sample mean is approximately Normal.
- Video: Sampling Distributions
Activity:
- Coin toss
- Toss a coin 10x
- Count the number of times the coin turns up “Heads”
- Enter the count on this spreadsheet
- Dice roll
- Roll a pair of dice (6-sided) 10x
- Add up the total for all 10 rolls
- Enter the total on this spreadsheet
- Demo CLT with Coin Flip and Dice Roll
