Question

4. Now imagine you are interested in testing whether a “power” nap can improve one’s memory. For your experiment, you get 60 participants each of whom is randomly assigned to either the control group (no power nap) or treatment group (power nap). For the treatment group, participants take a nap between 10 and 20 minutes after which they complete a task requiring them to read a short passage of text. After they read, they are given a 10-item, multiple-choice test for which they can earn up to 10 points (i.e., one point per question). Each item is designed to test how well one remembers important concepts and terms from the passage. In the control group, instead of taking a power nap, participants are asked to wait patiently for 10 minutes after which they are given the same task and test. Which statistical test should you use (2 points) and why (8 points)?

Answer 1

it is clear that we have two independent groups because a random sample of 60 people is divided into two parts and then diffrent treatments are given.

so, we have two independent samples with unknown population standard deviation.

When dividing 60 people into two groups, we have sample sizes n1 = n2 = 30

so, we can say that sample size is small and population standard deviation is unknown, this means t test for two independent samples can be used here.