Normal Distribution and Standard Error

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II. STATEMENT OF THE PROBLEM
As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth Medical Center in upstate New York investigated the relationship between geographic location, health status ( healthy or one or more comorbidities), and depression.  Random samples of 20 healthy individuals were selected from three geographic locations: Florida, New York, and North Carolina.  Then, each was given a standardized test to measure depression (higher test scores indicate higher levels of depression). Similarly, random samples of 20 individuals with one or more comorbidities (arthritis, hypertension, and/or heart ailment) were taken from the three geographic locations. They were also given the standardized test to measure depression. The researches would also like to know the following: a. Using descriptive statistics to summarize the data from the two studies, what are your preliminary observations about the depression scores? b. Using ANOVA on both data sets, what is the hypotheses being tested in both cases? What are your conclusions? c. Use inferences about individual treatment means where appropriate. What are your conclusions? d. Discuss extensions of this study or other analyses that you feel might be helpful

III. DESCRIPTIVE STATISTICS

1. Data

Table 1.1 shows the data of 60 individuals chosen for the study. Medical 1 reflects test scores from a standardized test to measure depression of healthy 20 individuals from Florida, 20 from New York and 20 from North Carolina. Medical 2 indicates the scores from another set of individuals but this time, with comorbidities.

| Data from Medical 1 |  | Data from Medical 2 | |Florida |New York |North Carolina |  |Florida |New York |North Carolina | |7 |11 |7 |  |12 |9 |12 | |7 |9 |3 |  |17 |15 |15 | |3 |7 |5 |  |17 |12 |18 | |8 |8 |11 |  |20 |16 |12 | |8 |7 |8 |  |21 |24 |14 | |8 |8 |4 |  |16 |18 |17 | |5 |4 |3 |  |14 |14 |8 | |5 |13 |7 |  |13 |15 |14 | |2 |10 |8 |  |17 |17 |16 | |6 |6 |8 |  |12 |20 |18 | |2 |8 |7 |  |9 |11 |17 | |6 |12 |3 |  |12 |23 |19 | |6 |8 |9 |  |15 |19 |15 | |9 |6 |8 |  |16 |17 |13 | |7 |8 |12 |  |15 |14 |14 | |5 |5...
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