The problems in this document may be used as extra review or practice for quizzes and exams. They are organized by chapter and are very similar in spirit to those found in the text. When referring to problems in this document, we will use the chapter number followed by the problem number. For example, Problem 1.3 refers to the third problem in the problem set for Chapter 1. The answers to these problems may be found in a companion document at this website.

Problems for Chapter 6

1. In Problem 1.3 we examined the pitch errors students made in trying to reproduce familiar songs and the so-called "lounge singer effect" wherein amateur singers tend to undershoot tones and to sing flat. We now consider this question again in the context of hypothesis testing. ( Based on data from Daniel J. Levitin, 1994, "Absolute memory for musical pitch: Evidence from the production of learned melodies," Perception & Pyschophysics, 56 (4) : 414 - 423.)

   Error (semitones)	Frequency
   -6	1
   -5	3
   -4	4
   -3	4
   -2	4
   -1	8
   0	12
   1	6
   2	1
   3	1
   4	1
   5	1
   6	0
   Total	46

   1. Rewrite the research hypothesis, "The students sing flat" as a hypothesis about the mean pitch error. Also state the null hypothesis in terms of the mean pitch error.
   2. Use a t test to answer this question.
   3. Suppose that you had used a sign test. Would your answer have been the same?
   4. Suppose that you had used a Wilcoxon signed-rank test. What would your conclusion be?
   5. Under what circumstances would each of the tests carried out be most appropriate? Which test do you think is most appropriate? You may wish to review your answer to Problem 1.3.

   

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