Question

Agri-Beef, Inc. is a large Midwestern farming operation. The company has been a leader in employing statistical techniques in its business. Recently, John Goldberg, operations manager, requested that a random sample of cattle be selected and that these cattle be fed a special diet. The cattle were weighed before the start of the new feeding program and at the end of the feeding program. John wished to estimate the average daily weight gain for cattle on the new feed program. Two hundred cattle were tested, with the following sample results: X = 1.2 pounds gain per day and S= 0.50 pounds gain per day.

1. Obtain a 90% confidence interval estimate for the true average daily weight gain.

2. Provide a 96% confidence interval estimate for the true average daily weight gain.

3. John is considering adopting this new diet. However, the weight gain comes at a 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 the hoof has been close to $0.20 a pound, would such a program be cost effective for Agri-Beef? Support your answer with calculations and statistical reasoning.

Answer 1

i)

ii)