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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?
The degrees of freedom for the x2-statistic
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Studies have shown that a positive association exists between educational level and annual salary; in other words, people with more education tend to make more money.
a. Does this finding mean that more education causes a person to make more money? Explain your answer.
b. Do you think there is a casual relationship between educational level and annual salary? Explain your answer.
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 owner | Part owner | Tenant | Total | |
| Under 50 | 70 | 44 | ||
| 50-179 | 492 | 130 | 38 | 660 |
| 180-499 | 198 | 368 | ||
| 500-999 | 51 | 84 | 14 | 149 |
| 1000& over | 41 | 114 | 17 | 172 |
| Total | 1521 | 541 |
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?
Job Satisfaction. A CNN/USA TODAY poll conducted by Gallul asked a sample of employed Americans the following question: "Which do you enjoy more, the hours when you are on your job, or the hours when you are not on your job?" The responses to this question were cross-tabulated against several characteristics, among which were gender, age, type of community, educational attainment, income, and type of employer. The data are provided on the WeissStats site. In each of Exercises 12.87-12.92, use the technology of your choice to decide, at the 5% significance level, whether an association exists between the specified pair of variables.
type of employer and response
The Quinnipiac University Poll conducts nationwide surveys as a public service and of research. This problem is based on the results of once such poll. Independent simple random samples of residents each in read (predominantly Republiclian), blue (predominantly Democratic) and purple (mixed) states were asked how satisfied they were with the way things are going today. The following table summarizes the responses.
At the significance level, do the data provide sufficient evidence to conclude that the satisfaction-level distributions differ among residents of red, blue and purple states?
We stated earlier that, if two variables are not associated, ther eis no point in looking for a casual relationship. Why is that so?
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