# Binomial distribution - Experimental results

## Binomial distribution - Experimental vs theoretical

Scenario: The Great Cookie Quality Conundrum
Background:
A local bakery prides itself on its chocolate chip cookies, claiming that exactly half the cookies in every batch have a special ingredient - a magic chip that makes them irresistibly delicious. To maintain their reputation, they want to ensure that this claim is statistically sound.
Objective:
As the head pastry data analyst, you have been tasked with verifying the bakery's claim using the principles of the binomial distribution.
Investigation Steps:
1. Hypothesis Setting:
- Null Hypothesis (H0): The proportion of cookies with the magic chip is 0.5 (p = 0.5).
- Alternative Hypothesis (H1): The proportion of cookies with the magic chip is not 0.5 (p ≠ 0.5).
2. Data Collection:
- You decide to randomly sample 20 cookies from each batch.
- You will then count the number of cookies with the magic chip.
3. Statistical Analysis:
- Use the binomial distribution with n = 20 and p = 0.5 to model your findings.
- Compare the experimental mean and variance to the theoretical values.
4. Decision Making:
- Based on the observed data, decide whether the bakery's claim holds up.
- Discuss the possible reasons for any discrepancies between the theoretical and experimental results.
Questions for Investigation:
1. Discovery Question:
- How would changing the proportion of magic chip cookies affect customer satisfaction and bakery sales?
2. Understanding Variance:
- What does the variance tell us about the consistency of the bakery's cookie-baking process?
3. Implications of Discrepancies:
- If the experimental mean is significantly different from 10, what could be some potential causes?
- What steps could the bakery take to address any inconsistencies found in the data?
4. Reflection:
- Why is it important for the bakery to understand the binomial distribution in quality control?
- How could this statistical approach be applied to other aspects of the bakery's operations?

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