Question

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 =

Answer 1

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