AP Statistics
Advanced Placement Statistics covering data analysis, probability, and statistical inference.
Statistical Inference: Confidence Intervals and Hypothesis Testing
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:
- Stating a null hypothesis (\(H_0\)) and alternative hypothesis (\(H_a\))
- Calculating a test statistic
- 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.
In a Nutshell
Use statistics to estimate values and test ideas with confidence.