Normal Distribution Curve for Visual Hypothesis Testing

This example visualizes how hypothesis testing is determined using a normal distribution curve: it links the significance level (α), the critical values, and the rejection/critical regions by showing the corresponding tail probabilities. The mathematical core includes the normal distribution parameters (μ, σ), the use of the inverse normal (InverseNormal) to compute quantiles/critical points for a given α, and probability evaluation by integrating the normal density over selected intervals (Integral). In GeoGebra construction, Textfield is used for dynamic labels and annotations, InputBox objects provide interactive control of inputs such as μ, σ and test thresholds, and InverseNormal together with Normal generates the critical points and the distribution curve. Segments highlight key connections to the curve, while the regions defined by critical boundaries (e.g., multiple threshold points) are integrated to obtain tail areas, often displayed as percentages with accompanying text objects. Suitable for secondary to early university learners studying probability and hypothesis testing, and for interactive classroom demonstrations.