The installation of a radon abatement device is recommended in any home where the mean radon concentration is 4.0 picocuries per liter (pCi/L) or more, because it is thought that long-term exposure to sufficiently high doses of radon can increase the risk of cancer. Seventy-five measurements are made in a particular home. The mean concentration was 3.72 pCi/L and the standard deviation was 1.93 pCi/L.

a. The home inspector who performed the test says that since the mean measurement is less than 4.0, radon abatement is not necessary. Explain why this reasoning is incorrect.

b. Because of health concerns, radon abatement is recommended whenever it is plausible that the mean radon concentration may be 4.0 pCi/L or more. State the appropriate null and alternate hypotheses for determining whether radon abatement is appropriate.

c. Compute the P-value. Would you recommend radon abatement? Explain.