FDA investigation of a meat-processing plant.

A particular meat-processing plant slaughters steers and cuts and wraps the beef for its customers. Suppose a complaint has been filed with the Food and Drug Administration (FDA) against the processing plant. The complaint alleges that the consumer does not get all the beef from the steer he purchases. In particular, one consumer purchased a cut and wrapped beef. To settle the complaint, the FDA collected data on the live weights and dressed weights of nine steers processed by a reputable meat processing plant (not the firm in question). The results are listed in the table.

LIVE WEIGHT DRESSED WEIGHT

x, pounds y, pounds

420 280

380 250

480 310

340 210

450 290

460 280

430 270

370 240

390 250

(a) Fit the model E(y) = 0 + 1x to the data.

(b) Construct a 95% prediction interval for the dressed weight y of a 300-pound steer.

(c) Would you recommend that the FDA use the interval obtained in part b to determine whether the dressed weight of 150 pounds is a reasonable amount to receive from a 300-pound steer? Explain.