Chapter 8.1, Problem 18P

Agriculture: Watermelon What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of $\bar{x}=\$6.88$ per 100 pounds of watermelon. Assume that $\sigma$ is known to be $1.92 per 100 pounds (Reference: Agricultural Statistics. U.S. Department of Agriculture).

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error?

(b) Sample Size Find the sample size necessary for a 90% confidence level with maximal margin of error E = 0.3 for the mean price per 100 pounds of watermelon.

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds.