Business Statistics

Introduction

To complete the statistical analysis and draw conclusions of a hospital stay and the associated charges for a normal child delivery, both Descriptive and Inferential statistical analysis will be applied to provide a better understanding of the data. In reference to Bryant/ Smith case 42 Hospital Charges, physicians have control over a substantial fraction of hospital costs; including the length of time a patient spends in the hospital, and which drugs and supplies are used in the patient's treatment. The sample data contains a sample of 289 records of patients, the number of days the patient spent in the hospital, charges to patients, according to two types of accounts, managed care insurance and commercial insurance.

The second section of the analysis continues with a descriptive statistics, as a science of describing the important aspects of a set of measurements ( Bowerman, 4th edition).Descriptive statistics aim to summarize a data set, rather than use the data to learn about the population that the data are thought to represent. Descriptive statistics provide simple summaries about the sample and the measures. Measures of central tendency, such as mean, median, mode and dispersion, such as range and standard deviation, are the main descriptive statistics. The mean is the most commonly used method of describing central tendency. To compute the mean, take the sum of the values and divide by the count.

The third section of the analysis continues with inferential statistics, which uses data gathered from a sample to make inferences about the larger population from which the sample was drawn. "Inferential statistics means the use of statistics to make inferences concerning some unknown aspect of a population from a sample of that population. A common method used in inferential statistics is estimation. In estimation, the sample is used to estimate a parameter, and a confidence interval about the estimate is constructed. Other examples of inferential statistics methods include hypothesis testing, linear regression and principle components analysis" (leonardoformamentis.net).

In conclusion, the we will analyze the statistical data looking at physician performance data to compare hospital charges with the patient's length of stay, type of insurance, and physician involved.

Analysis and Discussions

In Descriptive Statistics, the mean, standard deviation and sample size to determine the sample size for CHRGS and DAYS for both populations. The best way to approximate analysis is to first separate patients with Commercial Health Insurance and patients with Managed Cares by using data (sort) in Mini tab. Patients who have commercial insurance are 96, while patients who have Managed care Insurance are 193. The total number of patients from the data is 289.Below is the descriptive statistics in order to get a mean, standard deviation, and our sample size for CHRGS and DAYS for both populations:

Using Mini Tab to compute the results:

Table 1 Descriptive Statistics for Managed Care Insurance

CHARGES (CHRGS) DAYS

n 193 193

Mean 2966.4 2.3005

Sample Variance 1429844 1.1801

Sample Standard deviation 1195.8 1.0863

Minimum 929 1

Maximum 14898 14

Range 13969 13

Table 2 Descriptive Statistics for Commercial Insurance

Charges (CHRGS) DAYS

n 96 96

Mean 2714.3 2.0208

Sample Variance 449350.5 0.3364

Sample Standard deviation 670.3 0.5800

Minimum 902 1

Maximum 4933 3

Range 4031 2

It can be observed from both Table 1 and 2, shows that patients with managed care are significantly higher by 193 compared to patients with commercial insurance of 96. The data sample is 289, and the mean of $2966.4 is the average charge for patients having Managed care Insurance. The mean for Commercial Insurance patients are $ 2714.3, showing that Managed patients are being charged more than patients having Commercial Insurance. The difference of charges between both is $252.16. The average stay for both population shows that managed patients are slightly higher at 2.30 days compared to 2.02.

Inferential Analysis and Discussions

In inferential Analysis, a sample statistic is used to estimate the charges being patients with Managed care Insurance and Commercial insurance. Confidence Interval for a population mean is an interval constructed around the sample mean so that we are reasonably sure, or confident that this interval contains the population mean. Any Confidence interval for a population mean is based on what is called a confidence level. This confidence level is a percentage such as 95% or 99%, that expresses how confident we are that the confidence interval contains the population mean (Bowerman, pages 305, 307-310). Using Minitab for our computations, the following results are derived:

Table 3 Confidence interval - mean

Managed Care Insurance Charges and Days

Charges (CHRGS) DAYS

Confidence Level 95% (alpha .05) 95% (alpha .05)

Mean 2,966.44