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 = 8 children (9 years old) showed that they had an average REM sleep time of x1 = 2.5 hours per night. From previous studies, it is known that σ1 = 0.7 hour. Another random sample of n2 = 8 adults showed that they had an average REM sleep time of x2 = 1.70 hours per night. Previous studies show that σ2 = 0.6 hour. 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
difference μ1 − μ2. Round your answer to two
b. Find (or estimate) the P-value. (Round your answer to four decimal places.)
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