Agri-Beef, Inc. is large Midwestern farming operation. The company has been leader in employing statistical methods in its business. Recently, John Goldberg, operations manager, requested that random sample of cattle be chosen and that these cattle be fed a special diet. The cattle were weighed before the start of new feeding program and at the end of the feeding program. John wished to determine the average daily weight gain for cattle on new feed program. Two hundred cattle were tested, with the following sample results: X= 1.2 pounds gain for each day and S= 0.50 pounds gain per day.
a. Obtain a 95% confidence interval estimate for true average daily weight gain.
b. Provide a 90% confidence interval estimate for true average daily weight gain.
c. Determine the difference between two estimates found in parts a and b, and indicate the advantages and disadvantages of each.
d. John is considering adopting this new diet. But, the weight gain comes at price. To feed 200 cows for one month, the diet would cost approximately $1,000 more than their current feed program. If the price of beef on hoof has been close to $0.20 a pound, would such program be cost effective for Agri-Beef? Support your answer with calculations and statistical reasoning.