Confidence Interval (CI)
It’s a range where we think the real value is.
Instead of one number, we give two numbers (low, high)
Two Types
1. For Proportion (percent / yes-no)
\hat{p} \pm z^* \cdot \text{error}
2. For Mean (average)
\bar{x} \pm t^* \cdot \text{error}
What it means
Example:
95% CI = (40%, 50%)
👉 We are 95% sure the real value is between 40% and 50%
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Topic: Sampling Distributions
It’s about what happens when we take many samples from a
population.
Basic Idea
• You take a sample → calculate a statistic (like mean or
proportion)
• Repeat many times
• You get a distribution of those results
That’s called a sampling distribution
Key Point
The center of the sampling distribution = the true population
value
Spread (Standard Error)
• Shows how much results change between samples
• Formula (simple idea):
Bigger sample → less spread (more accurate)
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Topic: Inference for Means (AP Stats – Unit 7)
This unit is about using a sample mean to make conclusions
about the population mean
Main Idea
You don’t know the real average (µ), so you use your sample
(x̄ ) to:
• Estimate it
• Test if a claim is true
Two Main Tools
1. Confidence Interval (estimate)
\bar{x} \pm t^* \frac{s}{\sqrt{n}}
Gives a range for the true mean
2. Hypothesis Test (check a claim)
Steps (super simple):
1. State:
◦ H_0: claim (no change)
◦ H_a: what you want to prove
2.
3. Calculate t-score
4. Find p-value
5. Decide:
◦ small p-value → reject H_0
◦ large p-value → fail to reject