For each of the following scenarios, say whether the data should be treated as independent or paired samples. Explain briefly. If paired, explain what the pairing involves.
a) An efficiency expert claims that a new ergonomic desk chair makes typing at a computer terminal easier and faster. To test it, 30 volunteers are selected. Half of the volunteers will use the new chair and half will use their old chairs. Each volunteer types a randomly selected passage for 2 minutes and the number of correct words typed is recorded.
b) A real estate agent wants to know how much extra a fireplace adds to the price of a house. She selects 25 city blocks. In each block, she randomly chooses a house with a fireplace and one without and records the assessment value.
c) A manager wants to know if the mean productivity of two workers is the same. For each worker, he randomly selects 30 hours in the past month and compares the number of items produced.