Petroleum waste contamination. Accidental spillage and misguided disposal of petroleum wastes have resulted in extensive contamination of soils across the country. A common hazardous compound found in the contaminated soil is benzo(a)pyrene [B(a)p]. An experiment was conducted to determine the effectiveness of a method designed to remove B(a)p from soil (Journal of Hazardous Materials, June 1995). Three soil specimens contaminated with a known amount of B(a)p were treated with a toxin that inhibits microbial growth. After 95 days of incubation, the percentage of B(a)p removed from each soil specimen was measured. The experiment produced the following summary statistics: x = 49.3 and 5 = 1.5.
a. Use a 99% confidence interval to estimate the mean percentage of B(a)p removed from a soil specimen in which the toxin was used.
b. Interpret the interval in terms of this application.
c. What assumption is necessary to ensure the validity of this confidence interval?
d. Comment on whether the true mean percent removed could be as high as 50%.
e. Find and interpret a 90% confidence interval for the true variance in the percentages of B(a)p removed.