Question: The Environmental Protection Agency (EPA) recommends that the sodium content in public water supplies should be no more than 20 mg per liter (https://www.disabledworld.com/artman/publish/ sodiumwatersupply.shtml). Forty samples were taken from a large reservoir, and the amount of sodium in each sample was measured. The sample average was 23.5 mg per liter. Assume that the population standard deviation is 5.6 mg per liter. The EPA is interested in knowing whether the average sodium content for the entire reservoir exceeds the recommended level. If so, the communities served by the reservoir will have to be made aware of the violation.
a. Find the p-value for the test of hypothesis. Based on this p-value, would the communities need to be informed of an excessive average sodium level if the maximum probability of a Type I error is to be .05? What if the maximum probability of a Type I error is to be .01?
b. Test the hypothesis of part a using the critical-value approach and α = .05. Would the communities need to be notified? What if α = .01? What if is zero?