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 = 2.8 hours per night. From previous studies, it is known that σ1 = 0.6 hour. Another random sample of n2 = 10 adults showed that they had an average REM sleep time of x2 = 2.30 hours per night. Previous studies show that σ2 = 0.7 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.)

test statistic

critical value

P-value

Answer 1

z $\large \cong$ 1.72

P-value = 0.0427

Conclusion:-

P-value is less than alpha = 0.10 then conclude that the reject null hypothesis (Ho).

Therefore, there is sufficient evidence to support the claim.