Acid rain, caused by the reaction of certain air pollutants with rainwater, appears to be a growing problem in the northeastern United States. Acid rain affects the soil and causes corrosion on exposed metal surfaces. Pure rain falling through clean air registers a pH value of 5.7 (pH is a measure of acidity: 0 is acid, 14 is alkaline). Suppose water samples from 40 rainfalls are analyzed for pH and the sample mean is equal to 3.7 and the sample standard deviation is 0.5. Find a 99% confidence interval for the mean pH in rainfall and interpret the interval. What assumption must be made for the confidence interval to be valid ?