Question

A local reporter calls a researcher who has performed a study on the rates of diabetes, which generated statewide estimates for California as well as county-level estimates for all counties. The reporter is from a very small county in California, and has a difficult time understanding why the researcher won't say whether the small county is better or worse than the state average. The state point estimate is 5 percentage points higher than the county's point estimate, but the county's margin of error is 7.5 percentage points due to small sample size. How would you explain to the reporter why they shouldn't say that the county has a lower rate than the state?

Answer 1

It should not be concluded that the country has a lower percentage points than the state since the sample size is small for the country. The margin of error of the country is high, indicating that there is an overlap in the percentages between state and country although the point estimate for state is higher than country. Because of this overlap, it can't be said that country has a lower rate than the state. Also, increasing the sample size for the country might give a different picture.