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 11

1. In recent years, increased attention has been given to the ecology of small mammals considered from a landscape perspective. Investigations which have examined the effects of forest fragmentation and mammal dispersion in the clear-cut areas surrounding these fragments have demonstrated that landscape structure affects the dispersion and distribution of mammals in the area. In most cases, mammals are more abundant on the edge (e. g., the ecotonal area between the remaining forest and the clear-cut areas) than in any other type of landscape feature investigated. Possible reasons for this are the greater complexity of vegetation and the availability of two or more habitat types. Species inhabiting the edge are provided with a greater amount of food and cover than they would obtain from any single type of habitat. In one such study conducted in 1995 and repeated in 1998, three parallel transects of Sherman live traps were placed approximately 10 m apart in each of three study areas: a hardwood forest fragment, its edge, and a surrounding clear-cut area. ( See F. D. Martin, et al, "Role of edge effect on small mammal populations in a forest fragment," www.srs.gov/general/sci-tech/fulltext/tr2000103/tr2000103.html. )
   1. In 1995 the sampling effort was nearly double that of 1998 (almost twice as many traps used). Determine whether the distribution of mammals captured was independent of the year of capture.

      Year
      Location	1995	1998	Total
      Interior	26	12	38
      Edge	46	25	71
      Clear-cut	10	6	16

   2. For the 1998 study, the traps were ranked by numbers mammals captured over a 18-day period. Test whether there was a difference by site in small mammal captures (i.e., distribution) using the data reported below. If there was, determine which sites were different.

   Location	Interior	Edge	Clear-cut
   ni	10	10	10
   Rank sum Ri	132	218	115

   

2. In an elementary genetics experiment two fruit flies thought to be heterozygous for a recessive gene causing reduced wings (apterous) were mated together with the expectation that if they were, indeed, heterozygous they would produce progeny in a 3 wild type to 1 apterous ratio. Their progeny consisted of 17 wild type and 2 apterous flies. Use the binomial test to see if these results warrant rejection of the original assumption.

   

3. In Problems 1.3 and 6.1 we were interested in how the pitch errors made by students trying to reproduce familiar songs were distributed. (Based on data from Daniel J. Levitin, 1994, Absolute memory for musical pitch: Evidence from the production of learned melodies, Perception & Pyschophysics, 56 (4): 414423.)

   Xi Cum. freq. Rel. cum. freq. -6 1 0.022 -5 4 0.087 -4 8 0.174 -3 12 0.261 -2 16 0.348 -1 24 0.522 0 36 0.783 1 42 0.913 2 43 0.935 0 44 0.957 4 45 0.978 5 46 1.000 6 46 1.000

   1. One possible null hypothesis is that humans are not able to accurately recall actual pitches at all. In this case, one would expect that errors in pitch reproduction that subjects make would be uniformly distributed over the 12 one semitone subintervals in an octave. The shape of the error distribution would be rectangular with each bar about 1 / 12 = 0.083 units high. This does not seem to describe the actual error histogram. Test the null hypothesis that the errors are uniformly distributed using the Kolmogorov-Smirnov test. Be sure to use the cumulative uniform distribution when determining the test statistic. Suggestion: Use intervals of one semitone starting at 5.5 to match the histogram. Make use of the relative cumulative frequencies given above.
   2. If subjects have some pitch memory, we would expect the errors to be clustered about some mean value (near 0). Test the null hypothesis that the errors are normally distributed using the Kolmogorov-Smirnov test. (Note: = 1.0 semitones and s = 2.4 semitones.)
   3. Return to Problem 6.1. Which one-sample test was most appropriate? Can we conclude that the students are flat?