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 ofn 1 = 8 children (9 years old) showed that they had an average REM sleep time of x1 = 2.6 hours per night. From previous studies, it is known that σ1 = 0.6 hour. Another random sample ofn 2 = 8 adults showed that they had an average REM sleep time of x2 = 1.90 hours per night. Previous studies show that σ2 = 0.5 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 level of significance? State the null and alternate hypotheses. H 0: μ1 2;H 1: μ1 = μ2 H 0: μ1 = μ2;H 1: μ1 > μ2H 0: μ1 = μ2;H 1: μ1 ≠ μ2 H 0: μ1 = μ2;H 1: μ1 2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations. The Student'st. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Round your answer to four decimal places.)

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†....

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 ofn
₁ = 8 children (9 years old) showed that they had an average REM sleep time of x₁ = 2.6 hours per night. From previous studies, it is known that σ₁ = 0.6 hour. Another random sample ofn
₂ = 8 adults showed that they had an average REM sleep time of x₂ = 1.90 hours per night. Previous studies show that σ₂ = 0.5 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 level of significance?

State the null and alternate hypotheses.

H
₀: μ₁ <>₂;H
₁: μ₁ = μ₂
H
₀: μ₁ = μ₂;H
₁: μ₁ > μ₂H
₀: μ₁ = μ₂;H
₁: μ₁ ≠ μ₂
H
₀: μ₁ = μ₂;H
₁: μ₁ <>₂

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations. The Student'st. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to two decimal places.)

(c) Find (or estimate) theP-value. (Round your answer to four decimal places.)

Jun 02, 2022

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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†....

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