Question

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. ​

1) 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.
A. The data should be treated as independent samples because the samples are random.
B. The data should be treated as paired samples. Each pair consists of the number of correct words typed each minute°.
C. The data should be treated as paired samples. Each pair consists of a volunteer using each chair.
2) 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 equ al.
A. The data should be treated as paired samples. Each pair consists of the mean prices of different neighborhoods.
B. The data should be treated as paired samples. Each pair consists of the price of a house in each of the neighborhoods.
C. The data should be treated as independent samples because the samples are random within each neighborhood.
3) 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.
A. The data should be treated as independent samples because the samples are random.
B. The data should be treated as paired samples. Each pair consists of an hour in which the productivity of the two workers is compared.
C. The data should be treated as paired samples. Each pair consists of two hours in which the number of items produced is compared.

Answer 1

1) C

2) C

3) A

Explanation:

1) The right answer is C.

Each volunteer is a pair, consisting of the test of each chair. The difference can be compared for each individual and treated as a paired t-test.

2) The right answer is C.

There is no paired relation between the houses of each sample. There are two independent samples with the same sample size.

3) The right answer is A.

The hours are selected at random, so there is no relation between the hours picked for each worker. There are two indpendent samples with the same sample size.