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Category > Computer Science Posted 19 Sep 2017 My Price 9.00

Medical School of the University of Zurich,

Confidence Interval for μ1-μ2σ1and σ2 unknown

Alexander Borbely is a professor at the Medical School of the University of Zurich, where he is director of the Sleep Laboratory. Dr. Borbely and his colleagues are experts on sleep, dreams, and sleep disorders. In his book Secrets of Sleep, Dr. Borbely discusses brain waves, which are measured in hertz, the numberof oscillations per second. Rapid brain waves (wakefulness) are in the range of 16 to 25 hertz. Slow brain waves (sleep) are in the range of 4 to 8 hertz. During normal sleep, a person goes through several cycles (each cycle is about 90 minutes) of brain waves, from rapid to slow and back to rapid. During deep sleep, brain waves are at their slowest. In his book, Professor Borbely comments that alcohol is a poor sleep aid. In one study, a number of subjects were given 1/2 liter of red wine before they went to sleep. The subjects fell asleep quickly but did not remain asleep the entire night. Toward morning, between 4 and 6 A.M., they tended to wake up and have trouble going back to sleep.

Suppose that a random sample of 29 college students was randomly divided into two groups. The first group of n1= 15 people was given 1/2 liter of red wine before going to sleep. The second group of n2= 14people was given no alcohol before going to sleep. Everyone in both groups went to sleep at 11 P.M. The average brain wave activity (4 to 6 A.M.) was determined for each individual in the groups. Assume the average brain wave distribution in each group is moundshaped and symmetric. The results follow:

Group 1 (x1 values): n1= 15(with alcohol)

Average brain wave activity in the hours 4 to 6 A.M.

16.0

19.6

19.9

20.9

20.3

20.1

16.4

20.6

20.1

22.3

18.8

19.1

17.4

21.1

22.1

 

For group 1, we have the sample mean and standard deviation of

width=and  s1= 1.86

Group 2 (x2 values): n2= 14(no alcohol)

Average brain wave activity in the hours 4 to 6 A.M.

8.2

5.4

6.8

6.5

4.7

5.9

2.9

7.6

10.2

6.4

8.8

5.4

8.3

5.1

For group 2, we have the sample mean and standard deviation of

width=and  s2= 1.91

(a) Check Requirements Are the samples independent or dependent? Explain. Is it appropriate to use a Student’s t distribution to approximate the  width=distribution?          Explain.

(b) Compute a 90% confidence interval for μ1= μ2, the difference of population means.

(c) Interpretation What is the meaning of the confidence interval you computed in part (b)?

Answers

Maurice Tutor
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Status NEW Posted 19 Sep 2017 09:09 AM My Price 9.00

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