Question

In 1975 the journal Environmental News reported that a number of communities in Boston showed elevated levels of lead in the drinking water supplies. Water testing was done on a random sample of 248 households in these areas of Boston and results showed that 20% of the households had lead levels that were above the U.S. Public Health Service standard of 50 ppm. A nearby area that used anti-corrosives in its water supply as a preventative measure to reduce the leaching of lead from pipes into the water showed that 5% of 100 randomly selected households had lead levels in excess of the standard. Explain the approach you would use to evaluate whether there appeared to be an association (or difference in elevated lead levels) for the two communities. You don't have to do the calculation but must:

  

1. specify the null and alternative hypothesis

2. describe the statistical test or approach you would use

3. justify why you would use that test/approach.

4. identify the page in the text (or presentation & slide number) that contains the relevant equations.

Answer 1

Null Hypothesis H0: The true proportion of the households in Boston that had lead levels in excess of the standard is equal to the true proportion of the households in nearby area that had lead levels in excess of the standard.

Alternative Hypothesis Ha: The true proportion of the households in Boston that had lead levels in excess of the standard is greater than the true proportion of the households in nearby area that had lead levels in excess of the standard.

As we are comparing the sample proportions of two independent samples, we used two-proportion z-test.

We would use that two-proportion z- test because -

• The sampling method used for households in Boston and near by areas was simple random sampling.
• The samples of households from Boston and near by areas are independent of each other.
• Each sample includes at least 5 households with elevated lead levels and with no elevated lead levels i.
• Obviously the population is at least 20 times as big as the sample.

Select the page in the text (or presentation & slide number) that contains equations for two-proportion z-test.

Pooled proportion, p = (n1p1 + n2p2) / (n1 + n2)

Standard error of mean difference , SE =

Test statistic Z = (p1 - p2) / SE

where Z ~ N(0, 1) (Standard Normal distribution)