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Chapter 12: Q. 12.50 (page 501)

12.50 U.S. Hospitals. The American Hospital Association publishes 12.30 U.S. information about U.S. hospitals and nursing homes in Hospital Statistics. The following contingency table provides a cross classification of U.S. hospitals and nursing homes by type of facility and number of beds.

In the following questions, the term hospital refers to either a hospital or nursing home.


24 or fewer25-7475 or moreTotal
General260158635575403
Psychiatric24242471737
Chronic132236
Tuberculosis0224
Other25177208410
Total310201042606580

a. How many hospitals have at least 75 beds?

b. How many hospitals are psychiatric facilities?

c. How many hospitals are psychiatric facilities with at least 75 beds?

d. How many hospitals either are psychiatric facilities or have at least 75 beds?

e. How many general facilities have between 25 and 74 beds?

f. How many hospitals with between 25 and 74 beds are chronic facilities?

g. How many hospitals have more than 24 beds?

Short Answer

Expert verified

(a) 4260 hospitals are there.

(b)737 hospitals are there.

(c)471 hospitals are there.

(d)4256 hospitals are there.

(e)1586 hospitals are there.

(f)3 hospitals are there.

(g)6270 hospitals are there.

Step by step solution

01

Step 1. Given

The given contingency table:-


24 or fewer25-7475 or moreTotal
General260158635575403
Psychiatric24242471737
Chronic132236
Tuberculosis0224
Other25177208410
Total310201042606580
02

Step 2. Part (a)  Finding the number of hospitals having at least 75 beds

4260 hospitals are there.

03

Step 3. Part (b) Finding  hospitals which are  psychiatric facilities

737 hospitals are there.

04

Step 4. Part(c) Finding  hospitals which are psychiatric facilities with at least 75 beds.

471 hospitals are there.

05

Step 5. Part (d) Finding hospitals which are either  psychiatric facilities or have at least 75 beds

4256 hospitals are there.

06

Step 6. Part (e) Finding  general facilities have between 25 and 74 beds

1586 hospitals are there.

07

Step 7. Part (f) Finding  hospitals with between 25 and 74 beds are chronic facilities

3 hospitals are there.

08

Step 8. Part(g) Finding hospitals have more than 24 beds

6270 hospitals are there.

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Most popular questions from this chapter

Girls and Boys. One probability model for child gender is that a boy or a girl is equally likely to be born. If that model is correct, then, for a two-child family, the probabilities are 0.25,0.50, and 0.25 for two girls, one girl and one boy, and two boys, respectively. W. Stansfield and M. Carlton examined data collected in the National Health Interview Study on two-child families in the article "The Most Widely Published Gender Problem in Human Genetics" (Human Biology, Vol. 81, No. 1, pp. 3-11). Of 42,888 families with exactly two children, 9,523 had two girls, 22,031 had one girl and one boy, and 11,334 had two boys.

a) At the 1% significance level, do the data provide sufficient evidence to conclude that the distribution of genders in two-children families differs from the distribution predicted by the model described?

b) In view of your result from part (a), what conclusion can you draw?

In each of the given Exercises, we have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 to be satisfied. Note: The number of cells for a contingency table with m rows and n columns is m⋅n.

12.70 five and three

Table 12.4 on page 486 showed the calculated sums of the observed frequencies, the expected frequencies, and their differences. Strictly speaking, those sums are not needed. However, they serve as a check for computational errors.

a) In general, what common value should the sum of the observer frequencies and the sum of the expected frequencies equal? Ex plain your answer.

b) Fill in the blank. The sum of the differences between each observed and expected frequency should equal

c) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies does not equal the sample size, what do you conclude?

d) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies equals the sample size, can you conclude that you made no error in calculating the expected frequencies? Explain your answer.

School Enrollment. The Current Population Survey from the

U.S. Census Bureau provides data on school enrollment. The following contingency table shows school enrollment below postsecondary, in thousands, by level and gender.


MaleFemaleTotal
Nursery2,3312,3774,708
Kindergarten
1,997
Elementary16,50415,734
High School8,383
16,446
Total29,363

How many prisoners a. are in state facilities?

a. have at least a college education?

b. are in federal facilities and have at most an 8th-grade education?

c. are in federal facilities or have at most an 8th-grade education?

d. in local facilities have a postsecondary educational attainment?

e. who have a postsecondary educational attainment are in local facilities?

f. are not in federal facilities?

In each case, decide whether Assumptions 1and 2for using chi-square goodness-of-fit test are satisfied.

Sample size: n=100.

Relative frequencies:0.65,0.30,0.05.
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