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, 15 volunteers are selected. Using both the new chair and their old chair, each volunteer types a randomly selected passage for 2 minutes and the number of correct words typed is recorded.
b) A developer wants to know if the houses in two different neighborhoods have the same mean price. She selects 10 houses from each neighborhood at random and tests the null hypothesis that the means are equal.
c) A manager wants to know if the mean productivity of two workers is the same. For a random selection of 30 hours in the past month, he compares the number of items produced by each worker in that hour.