# Statistics

posted by
**student**
.

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¡ªeven 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.

So fay I have been ablet o answer a, but I have no idea about how to make a sketch. Help please!!

a) Null Hypoithesis ¦Ì=24

Alternative Hypothesis ¦Ì ¡Ù24

mean=25

Standard deviation=1.95229

t= ((25-24))/(1.19520/¡Ì8)=2.36649