Question

A researcher conducted an experiment to see if specific eye exercises can improve peripheral vision. A random sample of 5people was rated for peripheral vision on a scale from 1 to 20 where 9 is considered average and higher scores indicate better peripheral vision. The researcher wants to determine whether the eye exercises are related to the peripheral vision of the people. The 5 people followed the prescribed eye exercise program and then the same group was sampled and rated again. Are these samples dependent or independent?

Select the correct answer below:

A)These samples are independent because the samples are randomly selected and are from populations that are not related to each other.
B)These samples are dependent because the populations are related to each other.
C)These samples are dependent because the people were not randomly selected.
D) Not enough information is provided to determine independence.

Answer 1

The samples in the research study are dependent samples because they involve pre-test and post-test measurements of the same individuals' peripheral vision after following an eye exercise program.

Step-by-step explanation:

The samples in question are dependent samples because they involve the same group of individuals before and after they followed the prescribed eye exercise program. This means that each person's post-exercise score is directly related to their pre-exercise score, with the eye exercises being the possible cause for any change observed. This scenario does not represent independent samples, which would require two separate and unrelated groups.

Option B is correct because the samples consist of measurements taken from the same individuals at two different times, making them dependent because the second measurement is likely influenced by the first. In such cases, a paired or matched sample test is usually appropriate rather than tests meant for independent samples.