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 = 10 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that σ1 = 0.7 hour. Another random sample of n2 = 10 adults showed that they had an average REM sleep time of x2 = 2.20 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 decimal places.)


(B) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Answer 1

(A)

n1 = 10

1 = 2.9

1 =0.7

n2 = 10

2 = 2.2

2 = 0.6

The value of the sample test statistic is given by:

So,

The value of the sample test statistic = 2.40

(B)

By Technology, Cumulative Area Under Standard Normal Curve = 0.9918

So,

P - value = 1 - 0.9918 = 0.0082

So,

P - value = 0.0082