Management Report

Project Description:

The data was collected by the Department of Health and Social Services of the State of New Mexico and cover 52 of the 60 licensed nursing facilities in New Mexico in 1988. You are hired as an intern by the Dept. of Health and Social Services, and part of your job description includes statistical analysis of some of their data and writing reports to be used by the department in their operations. Write a detailed report on your findings to answer some of the questions they wish to have addressed below. Your report, addressed to the management, should be brief and you should refrain from using terminology that is too 'statistical' as this will be used by the management staff who might not be familiar with the details of these statistical methods. Therefore, ensure that your report will make sense to them and include only the necessary statistical details. Include all the detailed statistical working in an appendix section. Show all your working and include all the necessary graphical and statistical summaries to address each question posed.

Note: The Appendix does not serve as part of the report to be used by the Health and Social Sciences management staff, but is strictly for my purposes to see how you tackled each of the questions using the statistical methods discussed in class. Please be as detailed as necessary.

Disclaimer: This data is to be used for the purposes of this project only. Data source http://lib.stat.cmu.edu/DASL/Stories/nursinghome.html

Variable Names:

1. BED = number of beds in home
2. MCDAYS = annual medical in-patient days (hundreds)
3. TDAYS = annual total patient days (hundreds)
4. PCREV = annual total patient care revenue (hundreds)
5. NSAL = annual nursing salaries (hundreds)
6. FEXP = annual facilities expenditures ( hundreds)
7. RURAL = rural (1) and non-rural ( 0 ) homes

This project constitutes \(40 \%\) of the final grade and will be graded out of 100 points

Questions to be addressed:

1. The management staff is interested in some descriptive statistics of the annual nursing salaries.

1. Plot the histogram and boxplot for NSAL. Describe the overall pattern of the histogram / boxplot and comment on any deviations from the pattern, if any.
2. What is the five-number summary of NSAL? Use the \(1.5 \times IQR\) rule to check for outliers.
3. Find the mean and standard deviation of NSAL. Is it plausible that the nursing salaries can be described using the normal distribution (Plot the normality plot for NSAL and discuss this) ?

2. An association is expected between the number of beds at the home (BED) and the annual total patient care revenue (PCREV).

1. Plot a scatter plot that shows how the annual total patient care revenue can be explained by the number of beds at the home. Describe the overall pattern of the scatter plot. Are there any outliers or influential points?
2. Differentiate between rural and non-rural homes and plot the scatter plot for the same association above. Discuss any noticeable patterns, if any.
3. Fit a linear model to predict annual total patient care revenue based on the number of beds. Calculate the correlation, $r$, and coefficient of determination, $r^{2}$. Interpret these values.
4. Is a linear model valid for this data? Look at the scatter and residual plots and discuss the validity of a linear model.
5. The department is proposing to introduce two facilities in New Mexico; one with a capacity of 150 beds and a larger one with a capacity of 350 beds. Use the regression line in (c) to predict the annual total patient care revenue for each of these facilities.

3. As a follow-up to the descriptive analysis of the nurses' salaries in Question 1 , the management staff is interested in assessing if on average the facilities may be underpaying or over-paying their staff.

1. Suppose that the nursing salaries given serve as salaries for the entire population. What is the mean and standard deviation for NSAL?
2. You take a SRS of 23 homes (which is sufficiently large in this case). Find the following probabilities:

1. The probability that their average annual salary is below $\$ 190,000.00$. The nurses are underpaid if their average annual salary is below $\$ 190,000.00$
2. The probability that their average annual salary is above $\$ 700,000.00$. The nurses are overpaid if their average annual salary is above $\$ 700,000.00$

Price: $25.91

Solution: The downloadable solution consists of 14 pages, 1191 words and 13 charts.
Deliverable: Word Document