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Chapter 12: Q. 12.100 (page 518)

A chi-square homogeneity test is to be conducted to decide whether four populations are nonhomogeneous with respect to a variable that has eight possible values. What are the degrees of freedom for the x2-statistic?

Short Answer

Expert verified

The degrees of freedom for the x2-statistic=21

Step by step solution

01

Step 1. Given Information

A chi-square homogeneity test is to be conducted to decide whether four populations are nonhomogeneous with respect to a variable that has eight possible values.
That is,
Number of populations,r=4

Number of possible values for the variable,c=8

02

Step 2.  Finding the degrees of freedom for the x2-statistic

Degrees of freedom for the 蠂2-statistic is given by

df=(r-1)(c-1)=(4-1)(8-1)=(3)(7)=21

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Most popular questions from this chapter

In each of the given Exercises, we have presented a contingency table that gives a cross-classification of a random sample of values for two variables, x, and y, of a population. For each exercise, perform the following tasks.

a. Find the expected frequencies. Note: You will first need to compute the row totals, column totals, and grand total.

b. Determine the value of the chi-square statistic.

c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated.

Fear of Gangs. In the article "Growing Pains and Fear of Gangs" (Applied Psychology in Criminal Justice, Vol. 5, No. 2, pp. 139-164), B. Brown and W. Benedict examined the relationship between worry about a gang attack and actually being a victim of a gang attack. Interviews of a sample of high school students yielded the following contingency table.

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.

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?

12.51 Farms. The U.S. Department of Agriculture publishes information about U.S. farms in Census of Agriculture. A joint frequency distribution for number of farms, by acreage and tenure of operator, is provided in the following contingency table. Frequencies are in


Full ownerPart ownerTenantTotal
Under 50
7044
50-17949213038660
180-499198

368
500-999518414149
1000& over4111417172
Total1521541

a. Fill in the six missing entries.

b. How many cells does this contingency table have?

c. How many farms have under 50 acres?

d. How many farms are tenant operated?

e. How many farms are operated by part owners and have between 500 acres and 999 acres, inclusive?

f. How many farms are not full-owner operated?

g. How many tenant-operated farms have 180 acres or more?
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