For each of the following studies, indicate whether the data were collected in a paired manner and therefore require a paired analysis.

a. A farmer wants to know whether hand-milking or machine-milking tends to produce more milk from cows. He examines records of how much milk the cows have produced in the past, and orders them from most to least productive. For the top two milk producers, he randomly assigns one to hand-milking and the other to machine milking. He does the same for the next two and the next two and so on.
b. A reporter for a local newspaper wants to compare prices of grocery items at two stores. She selects 30 grocery items that are sold at both stores and records the price of each item at each store.

c. Are some diet programs easier to stick to than other? Researchers randomly assigned overweight people to one of four popular diets, and they recorded how many in each diet successfully completed the program for one year.

d. Does catnip have a negative effect on cats’ social interactions with other cats? A student went to the local animal shelter and observed a dozen cats. She counted how many negative interactions each cat had in a 15-minute period. Then she exposed each cat to catnip and counted how many negative interactions the cat had in the following 15-minute period.