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=10children (9 years old) showed that they had an average REM sleep time ofx₁=2.6hours per night. From previous studies, it is known that₁=0.6hour. Another random sample ofn₂=10adults showed that they had an average REM sleep time ofx₂=2.00hours per night. Previous studies show that₂=0.5hour. 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 level of significance?

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

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