Question

Cocaine addicts need cocaine to feel any pleasure, so perhaps giving them an antidepressant drug will help. A $3$-year study with $72$chronic cocaine users compared an antidepressant drug called desipramine with lithium (a standard drug to treat cocaine addiction) and a placebo. One-third of the subjects were randomly assigned to receive each treatment. At the end of the study, researchers recorded whether or not the subjects relapsed. Which of the following conditions must be satisfied to perform the appropriate chi-square test using the data from this study?

I. The population distribution is approximately Normal.

II. The treatments were randomly assigned.

III. The observed counts are all at least $5$.

a. I only

b. II only

c. III only

d. II and III

e. I, II, and III

Short answer

Option(b) is correct because only condition II. must be satisfied.

Step-by-step solution

Step  1 : Given information

We have to select which option is correct.

Simplification

Thechisquaretesthasthreeconditions:randomness,independence,andlargecounts.

The volunteers will be randomly assigned to a survey, satisfying the random sample criterion.

The sample size should be smaller than $10\%$of the total population in order to satisfy the requirement of independence. Because each survey's projected count is at least $5$, the criterion of a large count will be met.

In given options, only II must be satisfied. Hence, b is correct.