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 ofn₁=9children (9 years old) showed that they had an average REM sleep time ofx₁=2.9hours per night. From previous studies, it is known that₁=0.9hour. Another random sample ofn₂=9adults showed that they had an average REM sleep time ofx₂=2.00hours per night. Previous studies show that₂=0.7hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance.

a) What is the value of the sample test statistic? (Test the difference₁₂. Round your answer to two decimal places.)

b) Find (or estimate) theP-value. (Round your answer to four decimal places.)