Question

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?

Short answer

(a)

	Full owner	Part owner	Tenant	Total
Under 50	739	70	44	853
50-179	492	130	38	660
180-499	198	143	27	368
500-999	51	84	14	149
1000& over	41	114	17	172
Total	1,521	541	140	2,202

(b)There are 15 cells in contingency table.

(c)853,000 are the total number of farms

(d)140,000 are the number of farms that tenant operated

(e)84,000 are the number of farms.

(f)681,000 are the total number of farms

(g) 58,000 are total number of farms

Step-by-step solution

Step 1. Given

The given contingency table is

	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

Step 2. Part (a) Finding the missing entries

provided in the following contingency table. Frequencies are in

	Full owner	Part owner	Tenant	Total
Under 50	739	70	44	853
50-179	492	130	38	660
180-499	198	143	27	368
500-999	51	84	14	149
1000& over	41	114	17	172
Total	1,521	541	140	2,202

Step 3. Part (b) Determine the number of cells

There are 15 cells in contingency table.

Step 4. Part(c) Determine the number of farms less than 60 acres

853,000 are the total number of farms

Step 5. Part(d) Determine the number of farms that tenant operated

140,000 are the number of farms that tenant operated

Step 6. Part (e)  Determine farms do land owners own and own 500 hectares and 999 hectares, in total.

84,000 are the number of farms.

Step 7. Part (f) Determine the number of farms that are not full-owner operated

$2,202,000-1,521,000=681,000$ are the number of farms

Step 8. Part (g)  Determine tenant-operated farms have 180 acres or more 

$27,000+14,000+17,000=58,000$are the number of farms