An article in theNational 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.) State the null and alternative hypothesis

b.) Use thep-value approach to test the researcher's claim at= 0.05. List the p-value and state whether you are rejecting the null hypothesis and the reason.