MathIsimple

Random Sampling & Statistical Inference

Learn how to collect representative data through random sampling and use statistical inference to draw conclusions about populations from samples!

10th Grade
Statistics
~60 min
🎮 Interactive Activity: Sampling Method Identifier

Identify the sampling method!

Scenario:

Select every 10th person from a list
🎮 Interactive Activity: Confidence Interval Calculator

Calculate the confidence interval!

Given:

Sample mean = 50
Standard deviation = 10
Sample size = 25
Confidence level = 95%
1. Introduction to Sampling and Inference

Why Sampling?

It's often impossible or impractical to study an entire population. Instead, we study a sample and use statistical inference to draw conclusions about the population.

Key Terms:

  • Population: The entire group of interest
  • Sample: A subset of the population
  • Parameter: A numerical characteristic of the population
  • Statistic: A numerical characteristic of the sample
Example 1: Population vs Sample

Population: All students in a school (1000 students)

Sample: 100 randomly selected students

Population parameter: Average height of all students (unknown)

Sample statistic: Average height of 100 students (known, used to estimate parameter)

Example 2: Statistical Inference

From a sample of 100 students with average height 5'6", we infer that the population average is likely around 5'6" (with some margin of error).

2. Random Sampling
3. Sampling Methods
4. Statistical Inference
5. Confidence Intervals
6. Sampling Bias
7. Real-World Applications
8. Problem-Solving Strategies
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
Correct
0%
Score
1
What is the main purpose of random sampling?
2
Which sampling method divides the population into groups first?
3
What is a confidence interval?
4
If a 95% confidence interval for a mean is 45 to 55, what does this mean?
5
What is the z-score for a 90% confidence level?
6
What is statistical inference?
7
Which sampling method uses a fixed interval?
8
What happens to the margin of error as sample size increases?
9
What is the difference between a sample and a population?
10
Why is random sampling important?