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 = 9 children (9 years old) showed that they had an average REM sleep time of x1 = 2.7 hours per night. From previous studies, it is known that σ1 = 0.5 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.00 hours per night. Previous studies show that σ2 = 0.7 hour.
1. What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ1 − μ2. Round your answer to two decimal places.)
2. Find (or estimate) the P-value. (Round your answer to four decimal places.)
3. Find a 98% confidence interval for μ1 − μ2. (Round your answers to two decimal places.)
Upper Limit =
Lower Limit =
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