According to the U.S. Environmental Protection Agency (EPA), if more than 10% of homes in a city record over 15 parts per billion (ppb) of lead in their drinking water, the city exceeds Federal standards for lead in drinking water.
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Question 1
Based on your previous reading, why do you think the EPA monitors the amount of lead in drinking water?
Question 2
A 2015 Virginia Tech study reported that out of a sample of 252 homes in Flint, Michigan, 42 of them had over 15 ppb of lead in their drinking water.[1] At the 1% significance level, do the data indicate that the city of Flint exceeded the EPA standard?
- Write the null hypothesis in symbols and in a complete sentence.
- Write the alternative hypothesis in symbols and in a complete sentence.
- Verify that the conditions for the one-sample z-test for proportions have been met.
- Go to the DCMP Inference for Population Proportion tool at https://dcmathpathways.shinyapps.io/Inference_prop/. Calculate the test statistic and P-value.
- Will the null hypothesis be rejected? Explain.
- At the 1% significance level, do the data indicate that the city of Flint exceeded the EPA standard? Write the conclusion in a sentence.
Question 3
Why do you think a 1% significance level is used here? Why not 10%? Or 5%?
Question 4
Suppose our sample resulted in a P-value of 0.023. Would it be okay to make a conclusion at the 5% significance level instead?
- Lead testing results for water sampled by residents. (2015, September). Flint Water Study Updates. http://flintwaterstudy.org/information-for-flint-residents/results-for-citizen-testing-for-lead-300-kits/ ↵
