# 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.

#### Solution Summary

This solution shows step-by-step calculations to identify types of variables, linear prediction rule, predicted job rating for each scenario. A full statistical analysis is also conducted with a decision rule.