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 ?₁ = 12 children (9 years old) showed that they have an average REM sleep time of ?₁ = 2.5 hours per night with ?₁ = 0.6 hour. Another random sample of ?₂ = 20 adults showed that they had an average REM sleep time of ?₂ = 1.9 hours per night with s₂ = 0.5 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use ? = 0.01.

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Answer 1

Press STAT -> Tests

t = 3.0497

Decision based on P value
P - value = P ( t > 3.0497 ) = 0.0024
Reject null hypothesis if P value < α = 0.01 level of significance
P - value = 0.0024 < 0.01 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that  on average, children tend to have more REM sleep than adults.