Advanced Topics
In a nutshell: Use statistics to estimate values and test ideas with confidence.
## Making Conclusions from Data
Statistical inference lets us draw conclusions about populations from samples.
## Confidence Intervals
A confidence interval gives a range of values likely to include the true population parameter. For example, a 95% confidence interval means we are 95% confident the true value is in that range.
## Hypothesis Testing
Hypothesis testing helps us decide if a result is significant or just due to chance. The process involves:
1. Stating a null hypothesis (\(H_0\)) and alternative hypothesis (\(H_a\))
2. Calculating a test statistic
3. Deciding whether to reject \(H_0\) based on the evidence
## Real-World Impact
Scientists, doctors, and businesses use inference to make critical decisions based on data.
Examples
- A medical researcher tests if a new drug lowers blood pressure more than the standard treatment.
- A poll estimates the percentage of voters who support a candidate within a margin of error.