A problem that occurs with certain types of mining is that some by-products tend to be mildly radioactive and these products sometimes get into our fresh water supply. The EPA has issued regulations concerning a limit on the amount of radioactivity in supplies of drinking water. Particularly, the maximum level for naturally occurring radiation is 5 picocuries per liter of water. A random sample of 24 water specimens from a city’s water supply produced the sample statistics y̅ = 4.61 picocuries per liter and s  = .87picocurie per liter.

a. Do these data provide sufficient evidence to indicate that the mean level of radiation is safe (below the maximum level set by the EPA)? Test using α = .01.

b. Why should you want to use a small value of a for the test in part a?

c. Calculate the value of b for the test if μ_a = 4.5 picocuries per liter of water.

d. Calculate and interpret the p-value for the test.