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.

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 their knowledge. The experimental group has a mean of 38 on the

test (with an estimated population standard deviation of 3); the control group

has a mean of 35 (with an estimated population standard deviation of 5). Using

the .05 level, what should the experimenter conclude? (a) Use the steps of

hypothesis testing, (b) sketch the distributions involved, and (c) explain your

answer to someone who is familiar with the *t *test for a single sample but not

with the *t *test for independent means.

17. Do students at various universities differ in how sociable they are? Twenty-five

students were randomly selected from each of three universities in a region and

were asked to report on the amount of time they spent socializing each day with

other students. The result for University X was a mean of 5 hours and an estimated

population variance of 2 hours; for University Y, M = 4, S2 = 1.5 and for University

Z, M = 6, S2 = 2.5 What should you conclude? Use the .05 level.

(a) Use the steps of hypothesis testing, (b) figure the effect size for the study;

and (c) explain your answers to parts (a) and (b) to someone who has never had

a course in statistics.

11. Make up a scatter diagram with 10 dots for each of the following situations:

(a) perfect positive linear correlation, (b) large but not perfect positive linear

correlation, (c) small positive linear correlation, (d) large but not perfect negative

linear correlation, (e) no correlation, (f) clear curvilinear correlation.

For problems 12 to 14, do the following: (a) Make a scatter diagram of the

scores; (b) describe in words the general pattern of correlation, if any; (c) figure

the correlation coefficient; (d) figure whether the correlation is statistically significant

(use the .05 significance level, two-tailed); (e) explain the logic of what

you have done, writing as if you are speaking to someone who has never heard

of correlation (but who does understand the mean, deviation scores, and hypothesis

testing); and (f) give three logically possible directions of causality, indicating

for each direction whether it is a reasonable explanation for the correlation

in light of the variables involved (and why).

Stat 315 Week 5

12. Four research participants take a test of manual dexterity (high scores mean better dexterity)

and an anxiety test (high scores mean more anxiety). The scores are as follows.

Person |
Dexterity |
Anxiety |

1 | 1 | 10 |

2 | 1 | 8 |

3 | 2 | 4 |

4 | 4 | -2 |