Methods of Computation for Significance

A personnel psychologist studying adjustment to the job of new employees
found that employees' amount of education (in number of years) predicts ratings
by job supervisors two months later. The regression constant in the linear
prediction rule for predicting job ratings from education is 0.5 and the regression
coefficient is .40. (a) Indicate the predictor variable, and (b) the criterion
variable. (c) Write the linear prediction rule for this example. Indicate the predicted
job rating for employees with each of the following amount of education
(in years): (d) 8, (e) 10, (f) 17, (g) 19, and (h) 21.

A clinical psychologist has found that scores on a new depression scale predict
satisfaction with psychotherapy. The regression constant in the linear prediction
rule for predicting satisfaction from the depression score is 12 and the regression
coefficient is .4. (a) Indicate the predictor variable, and (b) the
criterion variable. (c) Write the linear prediction rule for this example. Indicate
the predicted satisfaction for people with each of the following depression
scores: (d) 8, (e) 6, (f) 5, (g) 3, and (h) 0.

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 5% 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.

Do students at various colleges differ in how sociable they are? Twenty-five
students were randomly selected from each of three colleges in a particular region
and were asked to report on the amount of time they spent socializing each
day with other students. The results for College X was a mean of 5 hours and
an estimated population variance of 2 hours; for College Y, M = 4, S2 = 1.5;
and for College 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 (a) and (b) to someone who has never
had a course in statistics.