Question One:
There are 936 teaching hospitals and 2094 non-teaching hospitals. The central assumption is that value “1” in the teaching_hopsital column is used for teaching hospitals, while value “0” is used for non-teaching hospitals.
Question Two:
T-test is kind of inferential statistic that can be used to determine if there is a substantial difference between two group s’ means (Reid, 2013). For this exercise, it is used to determine whether there is a substantial difference between the two types hospitals. The t-test outcomes show that there is a significant difference between teaching hospitals and non-teaching hospitals for most of the variables.
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Question Three:
The two type of hospitals have different net-benefits. Teaching hospitals have a net benefit of 2.30E+10 (23,000,000,000) while non-teaching hospitals have a net benefit of 1.81E+10 (18,100,000,000). This is an indication that teaching hospitals had better net benefits than non-teaching hospitals.
t-test
Teaching | Non-teaching | ||
N | 936 | 2094 | |
Mean | 2.45E+07 | 8.64E+06 | |
Standard Deviation | 5.22E+07 | 3.06E+07 | |
Numerator |
15860000 |
||
Denominator |
1832571.191 |
||
Variance 1 /n1 |
2.91115E+12 |
||
Variance 2 /n2 |
4.47163E+11 |
||
Sum |
3.35832E+12 |
||
Square root |
1832571.191 |
||
t |
8.654506891 |
The t-test indicates that there is a substantial difference between teaching and non-teaching hospitals. This is an indication that there is greater evidence against the null hypothesis.
Question Four:
Figure 1 : Hospitals-cost box plot
Figure 2 : Hospitals-revenues box plot
Based on the box plots, teaching hospitals have higher cost and revenue than non-teaching hospitals. Besides, cost and revenue box plots look similar.
Question Five :
Overall, findings show that teaching hospitals have better performance than non-teaching hospitals. This is because they have better investment and more resources. On average, teaching hospitals have more interns and more employees. This leads to more expenses, but also it translates to more revenues. Based on the t-test results, there was a significant difference between the two types of hospitals. The p-value for hospital net benefit is less than 0.05, meaning at a 95% confidence interval, the null hypothesis is rejected. This is an indication that there is a significant difference between teaching and non-teaching hospitals’ performance. The findings in this exercise can be used to support managerial decision making. They can be used to determine areas that teaching hospitals have been focusing on and areas that non-teaching hospitals have failed. That way, it is possible to make informed decisions that will help to improve hospital performance (Anderson, Sweeney, & Williams, 2010).
Descriptive statistics
Hospital Characteristics | Teaching | Non-Teaching | p-value | ||||
N | Mean | St. Dev | N | Mean | St. Dev | ||
1. Hospital beds | 936 | 549.03 | 604.74 | 2094 | 299.68 | 536.64 | 6.26E-27 |
2. Number of paid Employee | 929 | 2,457.05 | 2548.75 | 2080 | 869.81 | 1000.41 | 1.91E-71 |
3. Number of non-paid Employees | 30 | 57.09 | 30.48 | 30 | 27.66 | 32.80 | 6.6E-4 |
4. Interns and Residents | 617 | 124.90 | 162.81 | 308 | 41.53 | 53.25 | 6.93E-29 |
5. System Membership | 936 | 0.67 | 0.47 | 2094 | 0.58 | 0.49 | 1.61E-06 |
6. Total hospital cost | 936 | 3.93E+08 | 1.30E+10 | 2094 | 1.37E+08 | 7.77E+09 | 0.57 |
7. Total hospital revenues | 936 | 4.17E+08 | 1.40E+10 | 2094 | 1.45E+08 | 8.42E+09 | 0.58 |
8. Hospital net benefit | 936 | 2.45E+07 | 5.22E+07 | 2094 | 8.64E+06 | 3.06E+07 | 7.90E-18 |
9. Available Medicare days | 929 | 28825.60 | 24311.48 | 2086 | 11626.08 | 13968.37 | 1.09E-84 |
10. Available Medicaid days | 929 | 10372.87 | 13077.35 | 2056 | 3057.12 | 5501.95 | 5.45E-58 |
11. Total Hospital Discharge | 929 | 16649.57 | 13582.91 | 2088 | 6345.48 | 7649.33 | 1.07E-96 |
12. Medicare discharge | 929 | 5571.57 | 4256.33 | 2086 | 2455.25 | 2790.81 | 4.21E-87 |
13. Medicaid discharge | 929 | 2011.15 | 2307.38 | 2050 | 723.58 | 1219.18 | 1.69E-55 |
References
Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2010). Fundamentals of Business Statistics . Boston, MA: Cengage Learning.
Reid, H. M. (2013). Introduction to Statistics: Fundamental Concepts and Procedures of Data Analysis . Thousand Oaks, CA: SAGE Publications.