Household Lead Intervention Example

Imagine we want to lower the exposure of children to lead from paint in homes.

Your team has suggested repainting the interior of homes with known lead paint to prevent exposure.

Your team decides to try it on 100 homes and quantify the result.

Your population is the blood lead levels of children living in homes with lead paint. Let’s assume that we’ve measured lots of children in homes with lead paint and we know that the mean level of lead is 5 ug/dL and that the standard deviation is 2 ug/dL.

That population distribution looks like this:

Our question is: “Does repainting lower lead levels in children.” Our null hypothesis is: “Repainting does not affect lead levels.”

Our sample is 100 children in homes that have been repainted.

After repainting these homes and measuring the children, the mean lead level of the 100 children is 4.5 ug/dL.

To determine if this is likely or unlikely under the null hypothesis, we use the sampling distribution.

According to the central limit theorem, the sampling distribution will have the same mean and the standard error (standard deviation of the sampling distribution) will be narrower.

SE = \sigma_{pop} / \sqrt{N_{sample}} = 2/\sqrt{100} = 0.2

That sampling distribution looks like this:

The probability of this mean of 100 children being below 4.5 ug/dL is represented by the shaded area and is quite small.