PSY/315
March 18, 2013

Chapter 7
14.) Evolutionary theory often emphasizes that human have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24-hour cycle of sleeping and waking-even though 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 were no light from outside and no clocks or other indications of time. They could turn the lights on and off is they wish. After a month in the room, each individual tended to develop a study cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, and 25.
Using the 0 .5 level of significance, what should we conclude about the theory that 24 hours is the natural cycle? (That is, does the average cycling under these conditions differ significantly from 24-hour?) (a) Use the steps of hypothesis testing. (b) Sketch the distributions involved, (c) explain yourself to someone who has never had a course in statistics. (a) Steps of hypothesis testing 1. Restate the question as a research hypothesis and a null hypothesis about the populations. There are two populations

Population 1: people who are given the experimental test for 24 hours is the natural cycle.
Population 2: people who are given the experimental test in less than 24 hours is the natural cycle.

The null hypothesis: µ = 24
The alternative hypothesis: µ ≠ 24

2. Define the features of the compared distribution
Sample mean: 25 M = (∑X)/N = 200/8 = 25 Sample Standard deviation: 1.195229 SD √ SD^2 =

Find the estimated population variance. You first need to figure the sample mean, which is (25+27+25+ 23+24+25+26+ 25)/8 = 200/8 = 25. The estimated variance population is S^2 = SS/(N-1) = [( 25-25)^2 + ( 27-25)^2 + (25-25)^2 + (23-25)^2 + (24-25)^2 + (25-25)^2 +