This GeoGebra applet helps you visualize the key concepts of hypothesis testing — specifically how the two[br]types of error, the power of the test, and the significance level all interact with each other. You control four sliders, and the graph updates instantly so you can see the effects in real time.[br][br]You will see two bell curves, a dashed vertical line, three colored shaded areas, and four sliders at the bottom. The top-right corner shows the live values of α, β, and Power — these update as you move sliders.[br][br][br]Here are the steps on how to use this simulator:[br][br][b]Step 1: Read the starting values. [/b]Before touching anything, read and record the starting values shown on the simulator: [br][table][tr][td]α (significance level) [/td][td] [/td][/tr][tr][td] β (Type II Error)[br][/td][td][br][/td][/tr][tr][td] Power (1 − β)[br][/td][td] [/td][/tr][tr][td] μ₀ (null mean)[br][/td][td][br][/td][/tr][tr][td] μ₁ (true mean) [/td][td][br][/td][/tr][tr][td] σ (std deviation) [/td][/tr][/table][br][b]Step 2: Explore and change one slider at a time.[/b] Change only ONE slider at a time. After each change, observe what happens to the colored areas and the values in the top-right corner before moving the next slider.[br][br][b]Step 3: [/b][b]Read and interpret the top-right values. [/b]The three values in the top-right corner update automatically as you move any slider. [br][br][b]Step 4: Answer the guided questions. [/b]

[b]Use the simulator to answer these questions. Write your observations below each one.[/b]