Question 325884: Evolutionary theories often emphasize that humans have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24-hour cycle of sleeping and waking—even if they are not exposed to the usual pattern of sunlight. To test this notion, eight paid volunteers were placed (individually) in a room in which there was no light from the outside and no clocks or other indications of time. They could turn the lights on and off as
they wished. After a month in the room, each individual tended to develop a
steady cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23,
24, 25, 26, and 25. Using the .05 level of significance, what should we conclude about the theory that 24 hours is the natural cycle? (That is, does the average cycle length under these conditions differ significantly from 24 hours?) (a) Use the steps of hypothesis testing. (b) Sketch the distributions involved. (c) Explain your answer to someone who has never taken a course in statistics.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Their cycles at the end of the study were as follows: 25, 27, 25, 23,
24, 25, 26, and 25. Using the .05 level of significance, what should we conclude about the theory that 24 hours is the natural cycle? (That is, does the average cycle length under these conditions differ significantly from 24 hours?)
(a) Use the steps of hypothesis testing.
Ho: u = 24
Ha: u is not 24
---------------------
n = 8
xbar = 25 and s = 1.195
t(25)=(25-24)/[1.195/sqrt(8)] = 2.3669
---
p-value = 2*P(t > 2.3669 when df = 7) = 0.0498
Since the p-value is less than 5% reject Ho.
Since the p-value is so close to 5% conduct more testing
or conclude that you fail to reject Ho at the 1% level
of significance.
============================================================
(b) Sketch the distributions involved.
(c) Explain your answer to someone who has never taken a course in statistics.
----
I'll leave "b" and "c" to you.
Cheers,
Stan H.
|
|
|
