Question: In each experiment, determine whether the data are obtained independently or are paired. If the data are independent, indicate the two distinct populations. If the data are paired, indicate the common characteristic.
a. A surgeon is investigating the effect of physical therapy on patients who have had rotator-cuff injuries. Twenty-eight patients were selected at random. The range of motion in the affected arm was measured in each patient prior to starting physical therapy. After three weeks of consistent therapy, the range of motion in each patient was measured again. The data will be used to determine whether physical therapy has increased the mean range of motion.
b. A woodwork manufacturer has several lathes used for shaving parts. The accuracy of each is determined by measuring the production width of a designed 1-mm wood strip. Nine lathes were selected at random. The accuracy of each was measured. Then the gib screws on each lathe were adjusted, and the width of another 1-mm wood strip was measured. The data will be used to determine if the mean width before adjustment is different from the mean width after adjustment.
c. A random sample of sixty 20-year-old males and a random sample of forty-five 70-year-old males were obtained. The length of each person's right ear was measured (in inches). The data will be used to determine whether the mean ear length of a 70-year-old male is greater than the mean ear length of a 20-year-old male.
d. Modular homes are built in a closed, factory setting, indoors, and are not subject to adverse weather conditions. The quality control is often better than for on-site construction, but the cost may also differ. Ten different styles of homes were selected, and the cost of each built as a modular home and on-site was estimated. The data will be used to determine whether the mean cost of modular homes is greater than for on-site construction.
e. Random samples of 25 frequent flyers on United Airlines and on Delta Airlines were obtained. The total number of accumulated frequent-flyer miles for each person was recorded. The data will be used to determine whether the mean number of frequent-flyer miles is greater for United Airlines passengers than for Delta Airlines passengers.