Question

State whether you would describe each of the following as matched pair or independent samples. Explain your answers.

(a) You randomly select a group of companies and observe the profits they make before and after a carbon emission trading scheme is introduced.

(b) You compare the average time customers are kept waiting before being seated at restaurants in Melbourne’s central business district with waiting times at restaurants in Carlton.

(c) You record the running time of 50 athletes running a distance of 100m, first wearing one brand of running shoes, and again wearing another brand.

(d) You want to know whether people are more likely to go see a movie if they have seen the movie trailer beforehand. You randomly select a group of people who have seen a particular movie trailer, and observe the proportion that intend to see that movie at the cinema. You then randomly select a group of people from among those who have not seen the trailer for that particular movie, and observe the proportion that intend to see that movie at the cinema.

(e) You measure the life span (in years) of ant colonies in the desert compared to ant colonies in the jungle.

(f) You measure the number of calves a pod of whales has when they are in cold climates, as opposed to when the pod has migrated to warmer climates.

Answer 1

In (a) it is a matched pair design as you are observing the same companies before and after a scheme. In (b) it is an independent samples design as you are comparing two different locations. In (c) it is a matched pair design as you are recording the running times of the same athletes with different shoe brands.

Step-by-step explanation:

(a) In this scenario, you are observing the profits of companies before and after a carbon emission trading scheme is introduced. Since you are comparing the same companies and their profits before and after the intervention, this is a matched pair design. The profits before and after are dependent on each other.

(b) This scenario involves comparing the average waiting times at restaurants in Melbourne's central business district with waiting times at restaurants in Carlton. Since you are comparing two independent groups (restaurants in different locations), this is an independent samples design.

(c) Here, you are recording the running times of 50 athletes wearing one brand of running shoes and then wearing another brand. Since the same athletes are running with both shoe brands, this is a matched pair design.

(d) This scenario involves randomly selecting a group of people who have seen a movie trailer and a group of people who have not seen the trailer, and observing the proportion that intend to see the movie at the cinema. Since the groups are independent and not related, this is an independent samples design.

(e) This scenario involves comparing the life spans of ant colonies in the desert and ant colonies in the jungle. Since you are comparing ant colonies in different habitats, this is an independent samples design.

(f) This scenario involves measuring the number of calves a pod of whales has in cold climates compared to when they have migrated to warmer climates. Since you are comparing the same pod of whales in different climates, this is a matched pair design.