Question

Suppose we did a new experiment to gather data on the number of​ un-popped kernels of microwave popcorn. Each student in your class brings home two bags. One is put it in the freezer​ overnight, while the other is left on the kitchen counter overnight. Each bag is popped the next day and the number of​ un-popped kernels is recorded. Are these data paired or​ independent?

a. Paired
b. Independent

Answer 1

The data collected from the popcorn experiment are considered paired because each student compares two dependent samples: one bag placed in the freezer and another left on the counter, which are then popped and recorded by the same student. The correct answer is a. Paired.

Step-by-step explanation:

The data collected from the experiment you described, involving one bag of popcorn being placed in the freezer and one being left on the kitchen counter overnight, are paired. This is because the two bags of popcorn, frozen and unfrozen, belong to the same student and are treated as dependent samples.

The outcome of one could be related to the outcome of the other due to factors such as the microwave used, the environment, or the way the student counts the un-popped kernels.

In statistics, when comparing two sets of data, we can have either independent groups or matched pairs.

Since each student is popping both bags of popcorn themselves under presumably similar conditions (aside from the pre-popping treatment of freezing or not), we consider these samples as matched or paired.