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 ofn₁=11children (9 years old) showed that they had an average REM sleep time ofx₁=2.6hours per night. From previous studies, it is known that₁=0.6hour. Another random sample ofn₂=11adults showed that they had an average REM sleep time ofx₂=2.10hours per night. Previous studies show that₂=0.5hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a10%level of significance. Solve the problem using both the traditional method and theP-value method. (Test the difference₁₂. Round the test statistic and critical value to two decimal places. Round theP-value to four decimal places.)

test statistic_______

critical value_______

P-value________

Conclusion

Reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults.

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

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

Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults.

Compare your conclusion with the conclusion obtained by using theP-value method. Are they the same?

We reject the null hypothesis using the traditional method, but fail to reject using theP-value method.

The conclusions obtained by using both methods are the same.

These two methods differ slightly.

We reject the null hypothesis using theP-value method, but fail to reject using the traditional method.