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
inch. Assume
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
According to the U.S. National Weather Service, at any given moment of any day, approximately 2000 thunderstorms are occurring worldwide. Many of these storms include lightning strikes. Sensitive electronic equipment is used to record the number of lightning strikes worldwide every day. Twelve days were selected at random, and the number of lightning strikes on each day was recorded. The sample mean was
8.6 million. Assume the distribution of the number of lightning strikes per day is normal with
a. Find a 99% confidence interval for the mean number of lightning strikes per day worldwide.
b. Do you think the normality assumption in this problem is reasonable? Why or why not?