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Chapter 12: Q. 12.9 (page 491)
Why is the phrase "goodness of fit" used to describe the type of hypothesis test considered in this section?
The phrase "goodness of fit" is used because to determine how well the observed frequencies fit the expected frequencies by carrying out the hypothesis test.
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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?
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.
| State | Federal | Local | Total | |
| 8th grade or less | 149.9 | 10.6 | 66.0 | 226.5 |
| some high school | 269.1 | 12.9 | 168.2 | 450.2 |
| GED | 300.8 | 20.1 | 71.0 | 391.9 |
| High school diploma | 216.4 | 24.0 | 130.4 | 370.8 |
| Postsecondary | 95.0 | 14.0 | 51.9 | 160.9 |
| College grad and more | 25.3 | 7.2 | 16.1 | 48.6 |
| Total | 1056.5 | 88.8 | 503.6 | 1648.9 |
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 exeercises 12.57-12.59, use the technology of your choice to solve the specified problems.
The National Governors Association publishes information on U.S Governors in Governors' Political Afflitiation and Term of Office. Based on that document we obtain the data on region of reidence an political party given on WeissStats site.
a. Group the bivariate data for these two variables into a contingency table.
b. Determine the conditional distribution of region within each party and the marginal distribution of region.
c. Determine the conditional distribution of party within each region and the marginal distribution of party.
d. Are the variables "region" and "party" for U.S. governors associated? Explain your answer.
In each of Exercises 12.18-12.23, we have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distribution of the variable differs from the given distribution.
Distribution:
Observed frequencies:
Significance level
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.
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