# AP Statistics : How to find sampling distribution of a sample proportion

## Example Questions

### Example Question #1 : Sampling Distributions

A researcher wants to determine whether there is a significant linear relationship between time spent meditating and time spent studying. What is the appropriate null hypothesis for this study?      Explanation:

This question is about a linear regression between time spent meditating and time spent studying. Therefore, the hypothesis is regarding Beta1, the slope of the line. We are testing a non-directional or bi-directional claim that the relationship is significant. Therefore, the null hypothesis is that the relationship is not significant, meaning the slope of the line is equal to zero.

Explanation:

Explanation:

### Example Question #1 : Properties Of Single Sample Distributions

The president of a country is trying to estimate the average income of his citizens. He randomly samples residents and collects information about their salaries. A percent confidence interval computed from this data for the mean income per citizen is Which of the following provides the best interpretation of this confidence interval?

There is a percent probability that all the citizens of the country have an income  between and There is a percent probability that the mean of another sample with the same size will fall between and There is a percent probability that the mean income per citizen in the school is between and If he was to take another sample of the same size and compute a percent confidence interval, we would have a percent chance of getting the interval  percent of the citizens of the country have an income that is between and There is a percent probability that the mean income per citizen in the school is between and A confidence interval is a statement about the mean of the population the sample is drawn from so there is a percent probability that a percent confidence interval contains the true mean of the population. 