An article in the National Geographic News (“U.S. Racking Up Huge Sleep Debt,” February 24, 2005) argues that Americans are increasingly skimping on their sleep. A researcher in a small mid-western town wants to estimate the mean weekday sleep time of its adult residents. He takes a random sample of 80 adult residents and records their weekday mean sleep time as 6.4 hours. Assume that the population standard deviation is fairly stable at 1.8 hours.
a. Calculate the 95% confidence interval for the population mean weekday sleep time of all adult residents of this mid-western town.
b. Can we conclude with 95% confidence that the mean sleep time of all adult residents in this mid-western town is not 7 hours?