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Identify three ways in which the total number of observations of bivariate data can be obtained from the frequencies in a contingency table.

Short Answer

Expert verified

Three ways in which the total number of observations of bivariate data can be obtained from the frequencies in a contingency table are as follows :-

1. Summing the row totals

2. Summing the column totals

3. Summing the frequencies in the cells

Step by step solution

01

Step 1. Given information

A contingency table is a tabular representation of categorical data.

02

Step 3. Three ways

Three ways in which the total number of observations of bivariate data can be obtained from the frequencies in a contingency table are as follows :-

1. Summing the row totals

2. Summing the column totals

3. Summing the frequencies in the cells

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Most popular questions from this chapter

The Quinnipiac University Pol conducts nationwide surveys as a public service and for research. This problem is baed on the results of one such poll that asked independent random samples of American adults in urban, suburban, and rural regions, "Do you support or oppose requiring background checks for all gun buyers?" Here are the results.

At the 1%significance level, do the data provide sufficient evidence to conclude that a difference exists in the proportions of supporters among the three regions?

Regarding the expected-frequency assumptions for a chi-square goodness-of-fit test, a chi-square independence test, or a chi-square homogeneity test,

a. state them.

b. how important are they?

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?

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.

What are the small boxes inside the heavy lines of a contingency table called ?

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