Hypothesis Testing

Formulate and test claims. Adjust experimental samples size, mean, and standard deviation to compute Standard Errors, Z-test statistics, and P-values under normal distributions.

Interactive Sandbox

Z-Distribution Rejection Curves & Confidence Intervals

Select your hypothesis configuration on the right and adjust the sample statistics sliders. Observe in real-time if the calculated Z-statistic lands in the shaded red rejection zone, and compare it with the confidence interval overlap.

FAIL TO REJECT NULL HYPOTHESIS (P-value > α)

1. Hypothesis Parameters

Alternative (Ha):
Significance (α):

2. Sample Statistics

Sample Mean (&xbar;): 72.0
Sample Size (n): 50
Standard Dev (s): 10.0

3. Diagnostics Summary

Z-Test Statistic: Z = +1.41
Calculated P-Value: P = 0.0786
Standard Error (SE): SE = 1.41
Algebraic Solver

Hypothesis Testing Trace Walkthrough

Trace how the test statistic is evaluated against significance critical thresholds and confidence regions.

Trace Calculations Steps

Critical Thresholds Cheat Sheet


Evaluation

Inference & Testing Quiz

Evaluate your conceptual understanding of error rates, significance cutoffs, Z vs t stats, and p-value interpretations.

Question 1 of 5 Score: 0/0

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Correct Answer!

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Statistical Error Rules


  • Null Hypothesis (H0): The baseline assumption of no effect or no difference (e.g. $\mu = 70$).
  • Alternative Hypothesis (Ha): The claim we wish to test (e.g. $\mu > 70$).
  • Type I Error (False Positive): Rejecting $H_0$ when it is actually true. The probability of this is exactly $\alpha$ (the significance level).
  • Type II Error (False Negative): Failing to reject $H_0$ when $H_0$ is false. The probability of this is $\beta$.
  • Power (1 - β): The probability of correctly rejecting a false null hypothesis. Power increases as sample size $n$ increases.