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 Forty cattle were tested, with the following sample results: X = 1.3 pounds gain per day and S= 0.60 pounds gain per day.
8. 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 Forty cattle were tested, with the following sample results: X = 1.3 pounds gain per day and S= 0.60 pounds gain per day.
a. Obtain a 92% confidence
b. Provide a 98% confidence interval estimate for the true average daily weight gain.
c. Discuss the difference between the two estimates found in parts a. and b., and indicate the advantages and disadvantages of each.
d. John is considering adopting this new diet. However, the weight gain comes at a price. To feed 240 cows for one month, the diet would cost approximately $1,800 more than their current feed program. If the price of cattle has been around $0.25 a pound, would such a program be cost effective for Agri-Beef? Support your answer with calculations and statistical reasoning.
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