Question

US. Hospitals. Refer to Exercise 12.50.

	24 or fewer	25-74	75 or more	Total
General	260	1586	3557	5403
Psychiatric	24	242	471	737
Chronic	1	3	22	26
Tuberculosis	0	2	2	4
Other	25	177	208	410
Total	310	2010	4260	6580

a. Determine the conditional distribution of number of beds within each facility type.

b. Does an association exist between facility type and number of beds for U.S. hospitals? Explain your answer.

c. Determine the marginal distribution of number of beds for U.S. hospitals.

d. Construct a segmented bar graph for the conditional distributions and marginal distribution of number of beds. Interpret the graph in light of your answer to part (b),

e. Without doing any further calculations, respond true or false to the following statement and explain your answer. "The conditional distributions of facility type within number-of-beds categories are identical.

f. Determine the marginal distribution of facility type and the conditional distributions of facility type within number-of-beds categories.

g. What percentage of hospitals are general facilities?

h. What percentage of hospitals that have at least 75 beds are general facilities?

i. What percentage of general facilities have at least 75 beds?

Short answer

(a).

b.Yes, because the conditional distribution of the number of beds between the type of facility is not the same.

c.

	24 or fewer	25-74	75 or more	Total
General	0.048	0.294	0.658	1.000
Psychiatric	0.033	0.328	0.639	1.000
Chronic	0.038	0.115	0.846	1.000
Tuberculosis	0.000	0.500	0.500	1.000
Other	0.061	0.432	0.507	1.000
Total	0.047	0.305	0.647	1.000

d.

e. False , because the two variables are associated.

f.

	24 or fewer	25-74	75 or more	Total
General	0.839	0.789	0.835	0.821
Psychiatric	0.077	0.120	0.111	0.112
Chronic	0.003	0.001	0.005	0.004
Tuberculosis	0.000	0.001	0.000	0.001
Other	0.081	0.088	0.049	0.062
Total	1.000	1.000	1.000	1.000

g.82.1% of hospitals are general facilities.

h.83.5% of hospitals that have at least 75 beds are general facilities.

i.65.8% of general facilities have at least 75 beds.

Step-by-step solution

Step 1. Given

The given contingency table is :

	24 or fewer	25-74	75 or more	Total
General	260	1586	3557	5403
Psychiatric	24	242	471	737
Chronic	1	3	22	26
Tuberculosis	0	2	2	4
Other	25	177	208	410
Total	310	2010	4260	6580

Part a. Step 2. The conditional distribution of beds 

The distribution is

Part b. Step 3. Explanation

Yes, because the conditional distribution of the number of beds between the type of facility is not the same.

Part c. Step 4. Marginal distribution

	24 or fewer	25-74	75 or more	Total
General	0.048	0.294	0.658	1.000
Psychiatric	0.033	0.328	0.639	1.000
Chronic	0.038	0.115	0.846	1.000
Tuberculosis	0.000	0.500	0.500	1.000
Other	0.061	0.432	0.507	1.000
Total	0.047	0.305	0.647	1.000

Part d. Step 5. Solution

Part e. Step 6. Explanation

False , because the two variables are associated.

Part f. Step 7.  Marginal distribution

	24 or fewer	25-74	75 or more	Total
General	0.839	0.789	0.835	0.821
Psychiatric	0.077	0.120	0.111	0.112
Chronic	0.003	0.001	0.005	0.004
Tuberculosis	0.000	0.001	0.000	0.001
Other	0.081	0.088	0.049	0.062
Total	1.000	1.000	1.000	1.000

Part g. Step 8. Solution

82.1% of hospitals are general facilities.

Part . h. Step 9. Solution

83.5% of hospitals that have at least 75 beds are general facilities.

Part i. Step 10. Solution

65.8% of general facilities have at least 75 beds.