2. A psychologist at a private mental hospital was asked to determine whether there was a clear difference in the length of stay for patients with different categories of diagnosis. Looking at the...

2.  A psychologist at a private mental hospital was asked to determine whether there was a clear difference in the length of stay for patients with different categories of diagnosis.  Looking at the last four patients in each of the three major categories, the results (in terms of weeks of stay) were as follows:

Diagnosis Category

Affective Disorders                             Cognitive Disorders                Drug-Related Conditions

            7                                                          12                                                        8

            6                                                          8                                                          10

            5                                                          9                                                          12

            6                                                          11                                                        10

Using alpha = 0.05, is there a significant difference in length of stay among diagnosis categories?  Show all five steps of hypothesis testing.