Question

classify the two given samples as independent or dependent.
sample 1: the annual incomes for 51 adults whose ages are between 20 and 25
sample 2: the annual incomes for the same 51 adults when their ages are between 40 and 45

choose the correct answer below.
a. the two given samples are independent because the same people were sampled.
b. the two given samples are dependent because the same people were sampled.
c. the two given samples are independent because different people were sampled.
d. the two given samples are dependent because different people were sampled.

Explanation:

To determine if the samples are independent or dependent, we analyze the sampling:

• Sample 1 and Sample 2 use the same 51 adults (measured at different ages: 20 - 25 and 40 - 45).
• Dependent samples occur when the same (or related) subjects are measured in both samples, as the data points are linked (the income of a person at age 40 - 45 may relate to their income at 20 - 25).
• Independent samples would use completely different groups. Here, since the same people are sampled, the samples are dependent.

Option A is wrong (same people mean dependent, not independent). Option C is wrong (same people, not different). Option D is wrong (same people, not different). Option B correctly states the samples are dependent because the same people were sampled.

Answer:

B. The two given samples are dependent because the same people were sampled.