1.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 and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression. The data collected follow; higher test scores indicate higher levels of depression. These data are contained in the file "Medical1.csv". A second part of the study considered the relationship between geographic location and depression for individuals 65 years of age or older who had a chronic health conditionsuch as arthritis, hypertension, and/or heart ailment. A sample of 60 individuals with such conditions was identified. Again, 20 were residents of Florida, 20 were residents of New york, and 20 were residents of North Carolina. The levels of depression recorded for this study follow. These data are contained in the file named "Medical2.csv".

For the rest of this problem, we will solely use "Medical1.csv". If you wish to look further, particularly into two-way ANOVA, feel free to utilize the second data file on your own.

a)Use descriptive statistics to summarize the data from the first study; in particular, the sample mean for each location, the grand mean, the sample size for each location, the sample size for the entire dataset, the sample standard deviation for each location, and the sample standard deviation for the entire dataset.

Please copy your R code and the result and paste them here.

b)Clearly state the hypotheses being tested.

c)Use the descriptive summary data from part a) to compute SSE, its degree of freedom, and MSE.

d)Use the descriptive summary data from part a) to compute SSTR, its degree of freedom, and MSTR.

e)Use the descriptive summary data from part a) to compute SST and confirm that it is equal to the sum of SSE and SSTR.

f)Compute the test statistic for your test.

g)Compute the p value for your test.

Please copy your R code and the result and paste them here.

h)Suppose the significance level is set at 5%. What is your conclusion? Provide a practical interpretation of your conclusion in this case.

Use the function aov() in R to run the test directly to confirm your results above are correct.