What the exam asks
- Identify the appropriate inference procedure and define the population parameter in context.
- Verify the three conditions for inference (randomization, 10%, and normality/large counts) using specific numbers from the scenario.
- Determine the critical value for a given confidence level .
- Calculate the point estimate, standard error, margin of error, and confidence interval boundaries.
- Determine the minimum sample size required to achieve a specified margin of error.
Core ideas
Naming the procedure and defining the parameter
When estimating a single population proportion from a single sample, the official name is the one-sample -interval for a population proportion.
You must define the parameter with three required pieces: the word proportion, the response variable (what counts as a “success”), and the target population. Never use sample words like “surveyed” when defining : describe the whole population.
Conditions for inference
Before constructing the interval, check all three conditions in context:
| Condition | What to check and write | Why we check it |
|---|---|---|
| Random | State that the data come from a random sample of the population (quote the prompt). | Ensures is an unbiased estimator of . |
| 10% (Independence) | When sampling without replacement, verify that (the population is at least ). |