Kathryn’s sample consists of patients at a psychiatric clinic. In the clinic population, 40% of patients have depression, 28% have anxiety disorders, 15% have eating disorders, 10% have intellectual disabilities, and 7% have another diagnosis. Kathryn’s sample has 55 individuals with depression, 35 with anxiety disorders, 19 with eating disorders, 5 with intellectual disabilities, and 16 with another diagnosis. Conduct a statistical test to determine whether the proportion of individuals with each diagnosis in Kathryn’s study is representative of the population of clinic patients.

a. What is the null hypothesis for this study?

b. Is a one- or a two-tailed test appropriate for this example? Why?

c. How many degrees of freedom are in Kathryn’s data?

d. If α = .05, what is the χ²_crit value for the data?

e. Calculate the χ²_obs value.
f. Compare the χ²_crit value and the χ²_obs value. Should you reject or retain the null hypothesis in this example?

g. Calculate an odds ratio for each of the diagnosis groups. Interpret these odds ratios.