GeoGebra Classroom

# WORK IN PROGRESS - Need to check the code Binomial distribution - Type I and Type II errors

## WORK IN PROGRESS - Need to check the code Binomial distribution hypothesis testing

1. Hypothesis Setting:
• Null Hypothesis (H0​): The proportion of red gummy bears is 25% (p=0.25).
• Alternative Hypothesis (H1​): The proportion of red gummy bears is not 25% (p≠0.25).
2. Data Collection:
• Take a random sample of 10 bags from the production line.
• Count the number of red gummy bears in each bag.
3. Statistical Analysis:
• Use the binomial distribution B(10,0.25) to calculate the probability of finding different counts of red gummy bears if the machine is functioning correctly.
• Determine the critical value for a 5% significance level. What is the probability of making a Type I error (rejecting H0​ when it's true)?
4. Decision Making:
• Based on the observed data, decide whether to reject the null hypothesis.
• If a bag has more or less than 2-3 red gummy bears (assuming the critical region is similar to the applet), should you be suspicious?
5. Type II Error Exploration:
• Suppose the actual proportion of red gummy bears due to the malfunction is 30%. What would be the probability of a Type II error (accepting H0​ when it's false)?
6. Practical Implications:
• Discuss what a Type I and Type II error would mean in the context of the candy factory.
• What would be the consequences of each error type for the company?
7. Recommendations:
• Based on your findings, what recommendations would you make to the factory management?
• Should the machine be recalibrated, or is the variation within acceptable limits?
Questions for Investigation:
1. Discovery Question:
• How many red gummy bears would you need to find in a sample bag to become suspicious that the machine is malfunctioning?
2. Understanding Probability:
• What does a p-value represent in the context of red gummy bears in a bag?
3. Implications of Errors:
• If you make a Type I error, what does that mean for the gummy bear production line?
• If you make a Type II error, what implications does it have for the customers?
4. Reflection:
• How does the concept of statistical significance translate into real-world decisions in a factory setting?
• Why is it important to understand both Type I and Type II errors when making decisions based on statistical analysis?