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 = 11 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 ₁ = 0.9 hour. Another random sample of n₂ = 11 adults showed that they had an average REM sleep time of x₂ = 1.60 hours per night. Previous studies show that ₂ = 0.8 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance.

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

(b) will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? null is H₀: ₁ = ₂; H₁: ₁ > ₂. choose one

1. At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. 2. At the = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. 3. At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

(c) Interpret your conclusion in the context of the application. choose one

1. Fail to reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults. 2. Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults. 3. Reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults.