# WORK IN PROGRESS - Need to check the code Confidence interval (AI HL 4.16)

## WORK IN PROGRESS - Need to check the code The Wizard's Ingredient Mix

Scenario: The Wizard's Ingredient Mix
Confidence interval (known population variance)
Background:
In the magical realm of Algebrica, wizards use precise mixtures of ingredients for their spells. To ensure the potency of their spells, wizards must calculate the confidence intervals for the amount of each ingredient using the known population variance of their storeroom supplies.
Objective:
As an apprentice wizard, you are tasked with using the "Confidence Interval" applet to estimate the amount of dragon scale dust needed for the upcoming Full Moon Spell, ensuring your measurements are accurate and reliable.
Investigation Steps:
1. Measuring the Sample:
- Take a small sample of dragon scale dust and measure its mean amount.
- Enter the sample mean, population standard deviation, and sample size into the applet.
2. Setting the Confidence Level:
- Decide on a confidence level that will ensure the Full Moon Spell's success without wasting ingredients.
- Use the applet to calculate the confidence interval for the dragon scale dust amount.
3. Interpreting the Results:
- Analyze the calculated interval to determine the range in which the true mean amount of dragon scale dust is likely to fall.
- Ensure that the interval is precise enough for spellcasting requirements.
4. Reporting to the Master Wizard:
- Prepare a report for the Master Wizard explaining your findings and how confident you are in the measurements.
Questions for Investigation:
1. Discovery Question:
- How would the confidence interval change if the population variance was underestimated or overestimated?
2. Practical Implications:
- Why is it important for a wizard to have a precise confidence interval for spell ingredients?
3. Experimenting with Confidence:
- How does changing the confidence level impact the width of the confidence interval?
4. Reflection:
- Reflect on the role of statistical confidence intervals in other areas of magical practice and study.

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