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

- Author:
- Cliff Packman

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

- 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).

- Data Collection:
- Take a random sample of 10 bags from the production line.
- Count the number of red gummy bears in each bag.

- 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)?

- 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?

- 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)?

- 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?

- 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?

- Discovery Question:
- How many red gummy bears would you need to find in a sample bag to become suspicious that the machine is malfunctioning?

- Understanding Probability:
- What does a p-value represent in the context of red gummy bears in a bag?

- 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?

- 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?

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