Question

Dr. Park is interested in how the functioning of the brain changes with age and how this, in turn, affects older individuals’ memory abilities. She randomly selects 11 older and 16 younger adults to study pictures of landscapes presented for 5 seconds each. After a 10-minute rest period, both groups perform a visual recognition test. They view a series of pictures and categorize each as either "old" (part of the set they studied) or "new" pictures. While this test is occurring, researchers use fMRI to measure the participants’ brain activity. Dr. Park and her team notice that the older adults all produced similar amounts of activity during the task. The younger adults, on the other hand, showed much more diversity of brain activity. Some younger study participants had a large amount of activity, while others had much less. Would it be valid for Dr. Park to use the independent-measures t test to test whether the brain activity of younger adults is different from that of older adults during a visual recognition task?
a. Yes, because none of the assumptions of the independent-measures t test are violated.
b. Yes, because the independent-measures t test is a robust test. No, because the two groups studied are not independent.
c. No, because the two populations from which the samples are selected do not appear to have equal variances.

Answer 1

Answer:

Option C.  No, because the two populations from which the samples are selected do not appear to have equal variances.

Step-by-step explanation:

The variance measures how far a set of (random) numbers are spread out from their average value.

The fact that the younger adults show diversity in their brain activity while the older adults produce similar activities show that there are no equal variances in the two populations from which the samples are selected.

Therefore it would not be valid for Dr. Park to use the independent-measures t-test to test whether the brain activity of younger adults is different from that of older adults during a visual recognition task

Answer 2

Answer:

No, because the two populations from which the samples are selected do not appear to have equal variances.

Step-by-step explanation:

We know that in the given study the two groups studied are older and younger people. The samples are randomly selected and are independent of each other. The t-test is a robust test if the assumptions are followed. In the given study, we are given that the older adults produced a similar response, while the younger adults produced more of diverse brain activity. Therefore, the variance of younger adults would not be equal to the variance of older adults. Since one of the assumptions of the t-test is that the population of the two groups have same variance and here this assumption appears to be violated. Hence the correct option is:  No, because the two populations from which the samples are selected do not appear to have equal variances.