WIP Hypothesis testing (AI HL 4.18) for proportion using binomial distribution
The Great Bean Counting Contest
WORK IN PROGRESS - Need to check the code
Scenario: The Great Bean Counting Contest
Background:
In the whimsical town of Statistiville, an annual bean counting contest is held. The goal is to guess the proportion of magic beans mixed within a large sack of ordinary beans. The current belief is that the proportion of magic beans is 28.51%. To win, contestants must provide evidence that the true proportion is different.
Objective:
As a contestant and a savvy statistician, you are to use the Hypothesis Testing Applet to determine if there's sufficient evidence to reject the town's belief about the proportion of magic beans.
Investigation Steps:
1. Formulating Hypotheses:
- Null Hypothesis (H0): The proportion of magic beans is p = 0.2851.
- Alternative Hypothesis (H1): The proportion of magic beans is p ≠ 0.2851.
2. Gathering Data:
- Use the applet to simulate drawing samples of beans and counting the number of magic beans.
- Adjust the applet to the number of beans you've observed and the total beans tested.
3. Conducting the Test:
- Set your significance level to determine how strong the evidence must be to reject H0.
- Use the applet to calculate the probability of observing your sample proportion if H0 is true.
4. Making a Decision:
- Based on the applet's results, decide whether to reject H0 or fail to reject H0.
- Explain your reasoning and the implications of your decision.
Questions for Investigation:
1. Discovery Question:
- How does changing the significance level affect the outcome of your hypothesis test?
2. Considering Outcomes:
- What are the consequences of making a Type I error (rejecting H0 when it is true) in this context?
3. Real-world Implications:
- Discuss how hypothesis testing for proportions can be applied in fields like agriculture or quality control.
4. Reflection:
- Reflect on the role of sample size in the accuracy of hypothesis testing.