136 Chapter 5 Basic Concepts of Probability
5.17 Using Appendix Data Set or the file on the web named ADD.dat,
a. What is the probability that a male will have an ADDSC score greater than 50 if the
scores are normally distributed with a mean of 54.3 and a standard deviation of 12.9?
b. What percentage of the male sample actually exceeded 50?
5.18 Using Appendix Data Set, what is the empirical probability that a person will drop out of
school given that he or she has an ADDSC score of at least 60? Here we do not need to as-
sume normality.
5.19 How might you use conditional probabilities to determine if an ADDSC cutoff score in Ap-
pendix Data Set of 66 is predictive of whether or not a person will drop out of school?
5.20 Using Appendix Data Set scores, compare the conditional probability of dropping out of
school given an ADDSC score of at least 60, which you computed in Exercise 5.18, with
the unconditional probability that a person will drop out of school regardless of his or her
ADDSC score.
5.21 In a five-choice task, subjects are asked to choose the stimulus that the experimenter has
arbitrarily determined to be correct; the 10 subjects only make one guess. Plot the sampling
distribution of the number of correct choices on trial 1.
5.22 Refer to Exercise 5.21. What would you conclude if 6 of 10 subjects were correct on trial 2?
5.23 Refer to Exercise 5.21. What is the minimum number of correct choices on a trial necessary
for you to conclude that the subjects as a group are no longer performing at chance levels?
5.24 People who sell cars are often accused of treating male and female customers differently.
Make up a series of statements to illustrate simple, joint, and conditional probabilities with
respect to such behavior. How might we begin to determine if those accusations are true?
5.25 Assume you are a member of a local human rights organization. How might you use what
you know about probability to examine discrimination in housing?
5.26 In a study of human cognition, we want to look at recall of different classes of words
(nouns, verbs, adjectives, and adverbs). Each subject will see one of each. We are afraid that
there may be a sequence effect, however, and want to have different subjects see the differ-
ent classes in a different order. How many subjects will we need if we are to have one sub-
ject per order?
5.27 Refer to Exercise 5.26. Assume we have just discovered that, because of time constraints,
each subject can see only two of the four classes. The rest of the experiment will remain the
same, however. Now how many subjects do we need? (Warning: Do not actually try to run
an experiment like this unless you are sure you know how you will analyze the data.)
5.28 In a learning task, a subject is presented with five buttons. He must learn to press three spe-
cific buttons in a predetermined order. What chance does that subject have of pressing cor-
rectly on the first trial?
5.29 An ice-cream shop has six different flavors of ice cream, and you can order any combina-
tion of any number of them (but only one scoop of each flavor). How many different ice-
cream cone combinations could they truthfully advertise? (We do not care if the Oreo Mint
is above or below the Raspberry-Pistachio. Each cone must have at least one scoop of ice
cream—an empty cone doesn’t count.)
5.30 We are designing a study in which six external electrodes will be implanted in a rat’s brain.
The six-channel amplifier in our recording apparatus blew two channels when the research
assistant took it home to run her stereo. How many different ways can we record from the
brain? (It makes no difference what signal goes on which channel.)
5.31 In a study of knowledge of current events, we give a 20-item true–false test to a class of col-
lege seniors. One of the not-so-alert students gets 11 answers right. Do we have any reason
to believe that he has done anything other than guess?
5.32 Earlier in this chapter I stated that the probability of drawing 25 blue M&M’s out of 60
draws, with replacement, was .0011. Reproduce that result. (Warning, your calculator will