Question

Question 1: A certain county has 1,000 farms. Corn is grown on 100 of these farms but on none of the others. In order to estimate the total farm acreage of corn for the country, two plans are proposed. Plan I: a) Sample 20 farms at random. b) Estimate the mean acreage of corn per farm in a confidence interval. c) Multiply both ends of the interval by 1,000 to get an interval estimate of the total. Plan II: a) Identify the 100 corn-growing farms. b) Sample 20 corn-growing farms at random. c) Estimate the mean acreage of corn for corn-growing farms in a confidence interval. d) Multiply both ends of the interval by 100 to get an interval estimate of the total. On the basis of the information given, which of the following is the better method for estimating the total farm acreage of corn for the county? *

Answer 1

Plan II

Explanation:

A certain county has 1,000 farms.

Corn is grown on 100 of these farms but on none of the others.

Since corn is grown on only 100 of these farms, the population of interest is the 100 farms on which corn is grown.

Therefore, a better method for estimating the total farm acreage of corn for the county is Plan II.

a) Identify the 100 corn-growing farms.

b) Sample 20 corn-growing farms at random.

c) Estimate the mean acreage of corn for corn-growing farms in a confidence interval.

d) Multiply both ends of the interval by 100 to get an interval estimate of the total.