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Mathematics homework help

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Discussion and 2 replies-No 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.
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 condition such 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 Medical2.
 
Managerial Report

Use descriptive statistics to summarize the data from the two studies. What are your preliminary observations about the depression scores?
Use analysis of variance on both data sets. State the hypotheses being tested in each case. What are your conclusions?
Use inferences about individual treatment means where appropriate. What are your conclusions?

 
Discussion
Initial post prompt: Your Managerial Report serves as your initial post to the discussion forum. After responding to the requirements posed by the Managerial Report, also provide an example in your career in which you believe one of the lessons learned from the Case has been/could be applicable. Alternatively, if you don’t have/foresee direct experience relevant to your current position, what type of scenario can you anticipate occurring where you can utilize one of the lessons learned from examining this case?

Response post prompt: Consider Managerial Reports posted by two of your peers. One or both of your responses may be to Managerial Reports for a case problem different from your own. Think critically and ask open-ended questions. If you agree, consider their position and expand upon their ideas. Provide an additional perspective. If you disagree, provide your reasoning. Always be professional and courteous in your responses.

Post by classmate 1
 
Greetings all,
I chose to do the case study 1 which centered around a Medical center. The purpose involved us collecting data from those who have depression. Here are how the results went:

First I made sure to look at both samples and based on these samples, make a descriptive statistic on both of the findings. The first look went into the individuals aspect, where we looked to see which of these individuals are in good health. After looking at the variance between the 3 states to find out which had the lowest variation for depression. By our calculations I find that Florida had the lowest amount. New York was next up and finally North Carolina had the highest variance reported. 
When looking at the 2nd sample of individuals who are over 65 & have chronic illness we notice something interesting. We noticed that instead of what we see in the first sample, in this one North Carolina has the lowest variance. Another thing we noticed was that this time the state of Florida was the one with he 2nd lowest reported variance. Last but not least we see that New York has the highest. So overall, we look at the data and we can see that Florida has the lowest amount of depression out of all the states listed.

2. From what we see from our calculations, the means are equal to the same thing. By this, it means a Null Hypothesis.

And then, its possible that it is a Alternative Hypothesis because we noticed one mean significantly different. In sample 1, the P-value = 0.00814 < 0.05 at a 5% significance level, and the null hypothesis is only rejected meaning that there is significant difference in depression level among the 3 states. We noticed that in sample 2 the P-value = 0.4939 > 0.05 at a 5% significance level, and this is seen as the null hypothesis since its not rejected. And again, this means there is no difference in mean depression level among three states.

After all the results, I can confirm that sometimes the location has a real impact on the depression level reported on healthy individuals. But… at the same time, we noticed that the location will not have any impact on the depression level on individuals with an already present chronic illness.
Reference: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran Modern Business Statistics with Microsoft Excel 7th Edition

Post by classmate 2
  
Managerial Report

Initially, I assumed Florida would have the lowest levels of depression when related to geographic location because of the warmer climate and sunnier days, and New York with the highest because of the colder climate and less days with sun. I also assumed that people with chronic illnesses would have higher levels of depression as well. After analyzing the data, the group with the highest levels of depression on average was New York for both studies. The group with the lowest levels of depression on average for the first study was Florida, however, North Carolina was for the second study. Between the two studies, the second study that sampled people with chronic illnesses had significantly higher levels of depression than the people sampled in the first study. This included means that were almost triple for Floridians, and almost double for both New Yorkers and North Carolinians. This piece of data wasn’t overly surprising since chronic illnesses typically have a dramatic negative effect on a person’s quality and length of life. In examining the variance within each group, North Carolina had the highest variance in the first study and the lowest in the second study. These findings and data can be found on the attached spreadsheet on the pages labeled “Data Medical 1” for the first study and “Data Medical 2” for the second study.
I used Excel’s ANOVA Single Factor tool to analyze the variance on both data sets. This data can also be found on the pages labeled “Data Medical 1” for the first study and “Data Medical 2” for the second study. The null hypothesis for the first study is that the levels of depression are equal among the three different areas (Florida = New York = North Carolina). The alternative hypothesis is that the levels of depression are not equal among the three different areas. Similarly for the second study, the null hypothesis is that the levels of depression among people with chronic illnesses in the sampled three locations are equal. The alternative hypothesis is that the levels of depression among people with chronic illnesses in the sampled three locations are not equal. Using a 95% confidence interval, I would reject the null hypothesis in the first study since the p-value .0081 is less than .05. In the second study, the p-value .4939 is greater than .05, so I would not reject the null hypothesis.
We can assess from this information that regardless of geographic location, people with no chronic illnesses have lower depression levels while people with chronic illnesses have much higher depression levels. The impact of geographic location on people without chronic illnesses is minor but still acknowledged by the data.
I could see this type of data and analysis being useful in my line of work to calculate hiring rates and/or starting salaries by field of study. I can also see this type of information being very useful in many ways in the medical field to test how certain factors may affect a population’s health. Additionally, it could be used in the entertainment industry to compare numbers of podcast listeners, numbers of people watching a certain show, etc. I could realistically see this type of analysis being useful in almost any industry.

 

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