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 = 8 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 = 8 adults showed that they had an average REM sleep time of x₂ = 2.40 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 10% level of significance. Solve the problem using both the traditional method and the P-value method. (Test the difference μ₁ − μ₂. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.)

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


Z = 1.64

Test Criteria :-
Reject null hypothesis if


Result :- Reject Null Hypothesis

P value = P ( Z > 1.644 ) = 0.0501

Decision based on P value
P value = P ( Z > 1.644 ) = 0.0501
Reject null hypothesis if P value < level of significance
P - value = 0.0501 < 0.10 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that children tend to have more REM sleep than adults at 10% level of significance.