Question: Among the homeless, it has been suggested that alcohol dependency is positively related to levels of mental health dysfunction. To test this hypothesis, alcohol dependency was measured using the Alcohol Dependency Scale (ADS; ranging from 0 to 60); mental health dysfunction was measured using the Psychiatric subscale of the Addiction Severity Index (ASI-P; ranging from 0.00 to 1.00). For both scales, a lower score indicates a less serious problem. I gathered information on both scales from 10 randomly selected males, residing in a NYC shelter. Their data are as follows:

Individual ADS (X) ASI-P (Y)

1 40 .32

2 20 .30

3 10 .35

4 25 .45

5 30 .35

6 10 .27

7 25 .16

8 50 .40

9 43 .33

10 36 .70

(a) Conduct the appropriate test for my hypothesis.

(b) What can you conclude about the relationship between alcohol dependency and mental health dysfunction?

(c) The reliability of the ADS is .86 and the reliability of the ASI-P is .82. What is the true correlation between these two variables?

(d) Write a short paragraph describing the results.

(e) Suppose the parameter from problem 1 was based on a random sample of 310 homeless men. Retest the hypothesis.

(f) In addition to the sample size, what are the differences between problem 1 and 4?