Redo Problem 11(a) using the critical region method, and compare your results to those obtained using the P-value method.
Problem 11
REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 10 children (9 years old) showed that they had an average REM sleep time of 1 = 2.8 hours per night. From previous studies, it is known that σ1 = 0.5 hour. Another random sample of n2 = 10 adults showed that they had an average REM sleep time of 2 = 2.1 hours per night. Previous studies show that σ2 = 0.7 hour.
Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance.