Psy 315 Final
14. 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.
Part A.
Step 1.
Ho=M=24(null)
H1=M24(alternative)
Step 2. X | | | 25 | 0 | 0 | 27 | 2 | 4 | 25 | 0 | 0 | 23 | -2 | 4 | 24 | -1 | 1 | 25 | 0 | 0 | 26 | 1 | 1 | 25 | 0 | 0 |
x= 200 S2=10/7= 1.42857 S2M=S2/N=10÷7/8=0.17857 SM=Sm2= 0.422577
Step 3. (=.025, DF=7) =2.365 =.05 /2= .025 (two tailed test)
So if the sample > 1.895
We reject H0
Step 4.
Sample = 2.366
Step 5. Since 2.66>2.365 we will reject the null hypothesis/HO
Part B.
.
The results show that the average sleep cycle is not 24 hours. This allowed us to reject the null hypothesis. We used the data to determine if the average person’s sleep cycle was 24 hours. After examining the information we see that is not the case.
18. Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on
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.
Part A.
Step 1.
Ho=M=24(null)
H1=M24(alternative)
Step 2. X | | | 25 | 0 | 0 | 27 | 2 | 4 | 25 | 0 | 0 | 23 | -2 | 4 | 24 | -1 | 1 | 25 | 0 | 0 | 26 | 1 | 1 | 25 | 0 | 0 |
x= 200 S2=10/7= 1.42857 S2M=S2/N=10÷7/8=0.17857 SM=Sm2= 0.422577
Step 3. (=.025, DF=7) =2.365 =.05 /2= .025 (two tailed test)
So if the sample > 1.895
We reject H0
Step 4.
Sample = 2.366
Step 5. Since 2.66>2.365 we will reject the null hypothesis/HO
Part B.
.
The results show that the average sleep cycle is not 24 hours. This allowed us to reject the null hypothesis. We used the data to determine if the average person’s sleep cycle was 24 hours. After examining the information we see that is not the case.
18. Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on