# AP Statistics : Confidence and Proportion

## Example Questions

Explanation:

### Example Question #1 : How To Find Confidence Intervals For A Difference Between Two Proportions

In a simple random sample of  people,  are left-handed. Find a  confidence interval for the true proportion of left-handed people in the entire population.

The sample is not sufficiently large. A confidence interval cannot be used.

Explanation:

Step 1: Determine the approporiate formula. In this case, the statistic is a proportion because the question says 261 people out of 1000 are left-handed. We want to use a confidence interval for proportions. The equation is

Step 2: , or the sample proportion is equal to

Step 3: The questions asks for a 95% confidence interval. You can assume a normal distribution because of the large sample size. Therefore, in a normal distribution, 95% of the data is contained within .

Step 4: Substitue all the values into the equation to get the answer.

### Example Question #51 : Ap Statistics

A health insurance executive suspects that 50% of insurance applications are incomplete (i.e. critical data is missing from the application). He wants to gather a sample to estimate the true proportion. He wants to be within 5% of the true mean with 95% confidence.

What sample size does he need?

375

385

395

405

365