WORK IN PROGRESS - Need to check the code Confidence intervals AIHL 4.16 (using t-distribution)
WORK IN PROGRESS - Need to check the code The Potion Potency Puzzle
Scenario: The Potion Potency Puzzle
Confidence intervals (using t-distribution - Using sample standard deviation)
Background:
In the magical land of Statistica, potion-making is a precise science. Apprentice potion makers must learn to estimate the potency range of their concoctions. The Grand Alchemist has provided an applet using the t-distribution for apprentices to practice determining the confidence intervals of their potion potency.
Objective:
As an apprentice, your task is to use the applet to create confidence intervals for your latest potion batch to ensure its effects are within the expected potency range.
Investigation Steps:
1. Brewing the Potion:
- Brew your potion and measure its potency, which you will input as the sample mean in the applet.
2. Measuring Consistency:
- Determine the consistency of your potion's potency by calculating the sample standard deviation and entering it into the applet.
3. Setting the Sample Size:
- Input the number of potion samples you've tested to calculate the degrees of freedom for the t-distribution.
4. Calculating the Confidence Interval:
- Choose a confidence level that represents how sure you want to be about your potion's potency range.
- Use the applet to calculate the confidence interval, which will give you the range in which the true mean potency is likely to fall.
5. Analyzing the Results:
- Interpret the results provided by the applet to understand what the confidence interval means for your potion's effectiveness.
Questions for Investigation:
1. Discovery Question:
- How does changing the confidence level affect the width of the confidence interval?
2. Practical Application:
- Why is it important for potion makers to have a precise confidence interval for their products?
3. Experimenting with Samples:
- What would happen to the confidence interval if you increased the sample size?
4. Reflection:
- Reflect on the importance of statistics in the field of potion-making and other areas of magical study.