Question: Public Policy and Political Science Many chimney fires are caused by a buildup of creosote, a highly flammable material that forms in flues due to the condensation of certain gases. In an effort to promote fireplace and wood-stove safety, a town in Vermont has started a new inspection program. Forty homes with wood stoves were selected at random, and the amount of creosote buildup one foot from the top of the chimney was carefully measured. The resulting sample mean thickness was x¯ = 0.131 inch. Assume σ = 0.02 inch.
a. Find a 95% confidence interval for the true mean thickness of creosote buildup one foot from the top of chimneys.
b. One-eighth of an inch of creosote buildup is considered safe. If there is evidence to suggest that the true mean thickness is greater than 1 8 inch, the town will embark on an extensive safety program. Using the interval constructed in part (a), should the town stress greater safety? Justify your answer.