14. Evolutionary theories oftenemphasize that humans have adapted to their physi
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Question
14. Evolutionary theories oftenemphasize that humans have adapted to their physical environment.One such theory hypothesizes that people should spontaneouslyfollow a 24-hour cycle of sleeping and waking-even if they are notexposed to the usual pattern of sunlight. To test this notion,eight paid volunteers where placed (individually) in a room inwhich there was no light from the outside and no clocks or otherindications of time. They could turn the lights on and off as theywished. After a month in the room, each individual tended todevelop a steady cycle.
Their cycles at the end of thestudy were as follows: 25, 27, 25, 23, 24, 25, 26, and 25.
Using the 5% level of significance,what should we conclude about the theory that 24 hours is thenatural cycle? (That is, does the average cycle length under theseconditions differ significantly from 24 hours?) (a) Use the stepsof hypothesis testing. (b) Sketch the distributions involved. (c)Explain your answer to someone who has never taken a coursein statistics.
Explanation / Answer
H0: sample mean = 24 hrs Ha: sample mean does not equal 24 hrs. Sample mean: 25 Sample Stdev = sqrt(70) / 7 = 1.195 z = (25 - 24) / (1.195 / sqrt(8)) = 2.367 --> p = .9911(area tothe left) There is only a .89% chance of having a sample mean this big orlarger if the sample came from a population with mean 24. Thus, since this probability is so small, we guess that the mean isnot 24.
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