Many people with cocaine addictions also suffer from mood disorders like depression or a manic-depressive disorder. To aid in the process of trying to break a patient€™s addiction to cocaine, a common antidepressant known as lithium is often given to patients in drug treatment centers. A randomized, comparative experiment was performed to determine whether another commonly prescribed antidepressant, disipramine, could be used to reduce the likelihood of patients€™ using cocaine again or whether antidepressant therapy helped at all.11 The 72 patients selected for study over a 3-year period were randomly assigned to one of three treatments: disipramine, lithium, or a placebo. After the end of the 6-week treatment period, these patients were interviewed to deter-mine if they had been successful in stopping their cocaine habit. A success was defined as having stopped using cocaine for 3 weeks or more during the 6- week treatment period. The data from the study are shown in Table 6.12.
The null and alternative hypothesis can be written as
H0: pD = pL = pC
Ha: at least one treatment group has a different proportion of successes than the others
Table 6.12 Results from a study of the effect of treatment with different antidepressant drugs (or a placebo) on the success of cocaine addicts in remaining drug- free for at least 3 weeks during a 6-week treatment period.

Where pD, pL, and pC represent the true proportions of successes in the D, L, and C groups, respectively.
a. Was either the explanatory (row) or the response (column) variable fixed before the study was conducted?
b. Is this an example of an experiment or an observational study?
c. Use Part A to determine if a chi-square test of homogeneity or a test of independence is appropriate for this study.
d. Create a segmented bar chart for the data. e. Conduct a chi- square test to determine if this difference between success rates is likely to occur by chance. Calculate a table of expected counts assuming that the null hypothesis is true. (If the treatment group makes no difference in the success or failure of the patient in remaining free from cocaine, we would expect the success rates of all three groups to be the same.)
f. Are the sample sizes large enough to assume that the chi-square distribution is appropriate? Explain.
g. What are the test statistic, the degrees of freedom, and the p-value?
h. Can we conclude that for this group of 72 people the treatment did cause a difference in success rates?
i. These 72 people were not randomly selected from a larger population. Can we conclude that these results hold for a larger group of people?

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Success File Total 10 18 14 Disipramine (D) Lithium (L) Placebo/Control (C) 4 Total 24 24 20 24 24 48 72 6