What is Inferential Statistics?

Introduction to inferential statistics and statistical inference

Interactive Inferential Statistics Visualization

Welcome to the Inferential Statistics Explorer

This interactive visualization helps you understand inferential statistics including sampling distributions, confidence intervals, hypothesis testing, and p-values. Explore how sample statistics relate to population parameters.

What you can explore:

Sampling Distributions - Distribution of sample means
Confidence Intervals - Range estimates for population parameters
Hypothesis Testing - Z-tests and t-tests
P-values - Probability of observing test statistic
Rejection Regions - Critical regions for hypothesis tests

How to Use This Visualization

Interactive Features:

• Select Test Type - Choose confidence interval or hypothesis test
• Adjust Parameters - Change sample mean, size, standard deviation
• Set Significance Level - Control alpha or confidence level
• Toggle Visualizations - Show/hide distribution and rejection regions

What You'll See:

• Sampling Distribution (green curve) - Normal distribution of sample means
• Confidence Interval (blue) - Range estimate for population mean
• Rejection Regions (red) - Critical regions for hypothesis tests
• Test Results - Test statistic, p-value, and conclusion

Test Type

Show Distribution

Sample Mean (x̄): 100.0

Population Mean (μ₀): 100.0

Sample Size (n): 30

Standard Deviation (σ): 15.0

Confidence Level: 95%

Confidence Interval Results

95% Confidence Interval

[94.29, 105.71]

Sample Mean ± Margin of Error

Margin of Error

±5.71

t × SE = 2.09 × 2.74

Statistics Summary

Standard Error

2.739

σ / √n

Degrees of Freedom

n - 1

Sample Mean

100.00

Population Mean (H₀)

100.00

Key Concepts

Sampling Distribution: Distribution of sample means. Follows normal distribution (Central Limit Theorem).

Confidence Interval: Range estimate for population parameter. 95% CI means 95% of intervals contain true parameter.

P-value: Probability of observing test statistic or more extreme, assuming H₀ is true. Small p-value suggests evidence against H₀.

t vs z: Use t-test when population standard deviation is unknown (small samples). Use z-test when σ is known or n is large.

Hypothesis Testing Steps

1. State Hypotheses: H₀: μ = μ₀ vs H₁: μ ≠ μ₀

2. Choose Significance Level: α = 0.050

3. Calculate Test Statistic: t = 0.000

4. Find P-value: 1.0000

5. Make Decision: Fail to reject H₀ (p ≥ α)

6. Interpret: No evidence that population mean differs from μ₀

Lessons

Individual learning units

Lessons coming soon