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Chapter 12: Q. 12.62 (page 510)

To decide whether two variables of a population are associated, we usually need to resort to inferential methods such as the chi-square independence test. Why?

Short Answer

Expert verified

Since the data for the entire populaton is not usually variable, so we need to resort to inferential methods such as chi-square independent test.

Step by step solution

01

Step 1. Given Information.

Two variables of a population are associated.

02

Step 2. Explanation.

Since the data for the entire populaton is not usually variable, so we need to resort to inferential methods such as chi-square independent test.

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Most popular questions from this chapter

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?

Housing Foundations. The U.S. Census Bureau publishes information about housing units in American Housing Survey for the United States. The following table cross-classifies single-unit occupied housing units by foundation type and tenure of occupier. The frequencies are in thousands.

For single-unit occupied housing units:


OwnerRenterTotal
Full-basement22,9873,30126,288
Partial-basement7,5169908,506
Crawl-space14,2893,47717,776
Concrete slab21,0135,65126,664
Other9493341,283
Total66,75413,75380,507

a. How many have crawl spaces?

b. How many are owner occupied?

c. How many are rented and have full basements?

d. How many have a basement?

e. How many are either owner occupied or have a concrete slab?

Education of Prisoners. In the article "Education and Correctional Populations" (Bureau of Justice Statistics Special Report, NCJ 195670), C. Harlow examined the educational attainment of prisoners by type of prison facility. The following contingency table was adapted from Table 1 of the article. Frequencies are in thousands, rounded to the nearest hundred.


StateFederalLocalTotal
8th grade or less149.910.666.0226.5
some high school269.112.9168.2450.2
GED300.820.171.0391.9
High school diploma216.424.0130.4370.8
Postsecondary95.014.051.9160.9
College grad and more25.37.216.148.6
Total1056.588.8503.61648.9

How many prisoners

a. are in state facilities?

b. have at least a college education?

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

d. are in federal facilities or have at most an 8th-grade education? e. in local facilities have a postsecondary educational attainment

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

g. are not in federal facilities?

US. Hospitals. Refer to Exercise 12.50.


24 or fewer25-7475 or moreTotal
General260158635575403
Psychiatric24242471737
Chronic132226
Tuberculosis0224
Other25177208410
Total310201042606580

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?

Suppose that bivariate data are to be grouped into a contingency table. Determine the number of cells that the contingency table will have if the numbers of possible values for the two variables are

a. two and three.
b. four and three.
c. m and n.
See all solutions

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