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Chapter 12: Q. 12.1 (page 484)
What is meant by saying that a variable has a chi-square distribution?
If the distribution contains the shape of a special type of right skewed curve which is called the chi-square curve, then the variable is said to have a chi-square distribution. It is denoted by .
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If the observed and expected frequencies for a chi-square goodness-of-fit test, a chi-square independence test, or a chi-square homogeneity test matched perfectly, what would be the value of the test statistic?
A chi-square homogeneity test is to be conducted to decide whether a difference exists among the distributions of a variable of six populations. The variable has five possible values. What are the degrees of freedom for the x2-statistic?
The -table has entries for areas of and. In contrast, the -table has entries for those areas and for and Explain why the -values corresponding to these additional areas can be obtained from the existing -table but must be provided explicitly in the -table.
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?
Why is the phrase "goodness of fit" used to describe the type of hypothesis test considered in this section?
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