An article in the National Geographic News (February 24, 2005) reports that Americans are increasingly skimping on their sleep. A researcher wants to determine if Americans are sleeping less than the recommended 7 hours of sleep on weekdays. He takes a random sample of 150 Americans and computes the average sleep time of 6.7 hours on weekdays.

Assume that the population is normally distributed with a known standard deviation of 2.1 hours.

a. Use the p -value approach to test the researcher’s claim at α = 0.01.

b. Use the critical value approach to test the researcher’s claim at α = 0.01.