Question

Pitch memory of amusiacs. A team of psychologists and neuroscientists tested the pitch memory of individuals diagnosed with amusia (a disorder that impacts one’s perception of music) and reported their results in Advances in Cognitive Psychology (Vol. 6, 2010). Each in a sample of 17 amusiacs listened to a series of tone pairs and then were asked to determine if the tones were the same or different. In a first trial, the tones were separated by 1 second. In a second trial, the tones were separated by 5 seconds. Since the same subjects are tested, we do a Paired Difference Test of the difference in the scores between 1 second and 5 seconds. Scores in the two trials were compared for each amusiac. 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. We will treat these as our mean and standard deviation for a small sample single mean test. The Null is that the difference is zero. Based on theory, the researcher expects that the score is higher for 1 second compared with 5 seconds (i.e., the difference is positive). Carry out the test using a = .05. Is there evidence to support the theory?

Select correct alternative hypotheses for testing the theory.

a) mu < 0

b) mu > 0

c) mu NE 0

Calculate the value of the test statistic.  

Will you reject Ho or Accept Ho?

Answer 1

Option - b) mu > 0

The test statistic is

t= d - D sd/n

  

0.11 - 0 0.19/17

  

= 2.387

DF = 17 - 1 = 16

At 0.05 significance level, the critical value is t_0.95,16 = 1.746

Since the test statistic value is greater than the critical value(2.387 > 1.746), so we should reject H₀.