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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

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