Amusia is a congenital disorder that adversely impacts one's perception of music. Refer to the Advances in Cognitive Psychology (Vol. 6, 2010) study of the pitch memory of individuals diagnosed with amusia, Exercise. Recall that each in a sample of 17 amusiacs listened to a series of tone pairs and was asked to determine if the tones were the same or different. In the first trial, the tones were separated by 1 second; in a second trial, the tones were separated by 5 seconds. The difference in accuracy scores for the two trials was determined for each amusiac (where the difference is the score on the first trial minus the score on the second trial). The mean score difference was .11 with a standard deviation of .19.
a. In theory, the longer the delay between tones, the less likely one is to detect a difference between the tones.
Consequently, the true mean score difference should exceed 0. Set up the null and alternative hypotheses for testing the theory.
b. Carry out the test, part a, using α = .05. Is there evidence to support the theory?