9 Statistics Problems

11. For the following scores, find the (a) mean, (b) median, (c) sum of squared
deviations, (d) variance, and (e) standard deviation:
2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 1, 4, 3, 4, 2, 1, 0

12. For the following scores, find the (a) mean, (b) median, (c) sum of squared
deviations, (d) variance, and (e) standard deviation:
1,112; 1,245; 1,361; 1,372; 1,472

13. For the following scores, find the (a) mean, (b) median, (c) sum of squared
deviations, (d) variance, and (e) standard deviation:
3.0, 3.4, 2.6, 3.3, 3.5, 3.2

14. On a standard measure of hearing ability, the mean is 300 and the standard deviation
is 20. Give the Z scores for persons who score (a) 340, (b) 310, and
(c) 260. Give the raw scores for persons whose Z scores on this test are (d) 2.4,
(e) 1.5, (f) 0, and (g) -4.5.

15. A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative
ability. For the verbal ability test, the mean for people in general is 50 and the
standard deviation is 20. For the quantitative ability test, the mean for people in
general is 0 and the standard deviation is 5. Which is this person's stronger ability:
verbal or quantitative? Explain your answer to a person who has never had a
course in statistics.

16. A psychologist interested in political behavior measured the square footage of the
desks in the official office of four U.S. governors and of four chief executive officers
(CEOs) of major U.S. corporations. The figures for the governors were 44, 36,
52, and 40 square feet. The figures for the CEOs were 32, 60, 48, and 36 square
feet. (a) Figure the means and standard deviations for the governors and for the
CEOs. (b) Explain, to a person who has never had a course in statistics, what you
have done. (c) Note the ways in which the means and standard deviations differ,
and speculate on the possible meaning of these differences, presuming that they
are representative of U.S. governors and large corporations' CEOs in general.

21. Payne (2001) gave participants a computerized task in which they first see a
face and then a picture of either a gun or a tool. The task was to press one button
if it was a tool and a different one if it was a gun. Unknown to the participants
while they were doing the study, the faces served as a "prime" (something that
starts you thinking a particular way); half the time they were of a black person
and half the time of a white person. Table 2-9 shows the means and standard deviations
for reaction times (the time to decide if the picture is of a gun or a tool)
after either a black or white prime. (In Experiment 2, participants were told to decide
as fast as possible.) Explain the results to a person who has never had a course in
statistics. (Be sure to explain some specific numbers as well as the general principle
of the mean and standard deviation.)

22. Suppose you want to conduct a survey of the attitude of psychology graduate students
studying clinical psychology toward psychoanalytic methods of psychotherapy.
One approach would be to contact every psychology graduate student you
know and ask them to fill out a questionnaire about it. (a) What kind of sampling
method is this? (b) What is a major limitation of this kind of approach?

25. You are conducting a survey at a college with 800 students, 50 faculty members,
and 150 administrators. Each of these 1,000 individuals has a single listing in
the campus phone directory. Suppose you were to cut up the directory and pull
out one listing at random to contact. What is the probability it would be (a) a student,
(b) a faculty member, (c) an administrator, (d) a faculty member or administrator,
and (e) anyone except an administrator? (f) Explain your answers to
someone who has never had a course in statistics.