Case C3 Ch 12 Examining the Hospital Database This database

Case C3 Ch. 12: Examining the Hospital Database

This database contains observations for 11 variables on U.S. hospitals. These variables include Geographic Region, Control, Service, Number of Beds, Number of Admissions, Census, Number of Outpatients, Number of Births, Total Expenditures, Payroll Expenditures, and Personnel.

Geographic Region variable is coded from 1 to 7, and the numbers represent the following regions:

1 = South

2 = Northeast

3 = Midwest

4 = Southwest

5 = Rocky Mountain

6 = California

7 = Northwest

Control is a type of ownership. Four categories of control are included in the database:

1 = government, nonfederal

2 = nongovernment, not-for-profit

3 = for-profit

4 = federal government

Service is the type of hospital. The two types of hospitals used in this database are:

1 = general medical

2 = psychiatric

Total Expenditures and Payroll variables are in units of $1,000.

Question: The administrators would like you to use the database to answer this question:

Is the type of ownership independent of the type of hospital? Use = 0.05 significance level.

Directions: Be sure to include in your memo (for each question):

[10pts] The tables of observed and expected frequencies.

[2pts] The test that should be used and the justification for using it.

[2pts] The null and alternative hypotheses.

[2pts] The test statistic.

[2pts] The p-value (or critical value if the rejection region method is used).

[2pts]The decision based on the PLAYR rule (or critical value).

[5pts]Plain language conclusions

Solution

From the data, prepare a contigency table for the variables type of ownership and type of hospital.

Null hypothesis: Type of owernership and type of hospital are independent.

Alternative hypothesis:Type of owernership and type of hospital are not independent.

The expected frequencies and chi-square statistic are computed in the following table.

Pearson Chi-Square = 15.474, DF = (2-1)*(4-1) = 3, P-Value = 0.001

Since P-value is less than 0.05 we reject the null hypothesis. Hence we conclude that type of hospital and type of owner ship are independent.