Appendix A
Additional Problems

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 10

  1. Because adult male African elephants, Loxodonta africana, continue to grow in height and weight, it is thought that older males are generally more dominant to younger ones. Mature males have sexually active musth periods and inactive nonmusth periods. During musth, males announce their sexually agressive state with infrasonic calls, temporal gland secretions, and urine dribbling. As part of a study to examine how male elephants use these signals to assess other males, 28 males born between 1935 and 1962 were ranked by dominance. (Based on data reported in Joyce H. Poole, "Signals and assessment in African elephants: Evidence from playback experiments," Animal Behaviour, 1999, 58 (1) : 185193.)

    Dominance
    rank

    Year of
    birth

    1 1935
    2 1939
    3 1940
    4 1935
    5 1945
    6 1945
    7 1945
    8 1947
    9 1945
    10 1945
    11 1946
    12 1950
    13 1952
    14 1950
    15 1948
    16 1953
    17 1953
    18 1951
    19 1953
    20 1953
    21 1953
    22 1956
    23 1956
    24 1957
    25 1957
    26 1960
    27 1961
    28 1962

    1. Determine the strength of the correlation between dominance and age in male African elephants by calculating Kendall's T for these data.
    2. Test the hypothesis Ha: T > 0 and interpret the result.

  2. a.   The average oral vocabulary size of children at various ages is given in the table below. The 
    scatterplot shows a clear relationship, but is it linear? If so, describe it with a mathematical 
    model, i. e., a regression line equation. Use analysis of variance to test H0: ß = 0. Also 
    calculate a 95% confidence interval for ß, if appropriate. (HSDS, #346)

        b.    Calculate û Y | 5.5 and its 95% confidence interval. Would you say a five-and-one-half 
    year-old with a vocabulary of 2000 words is in the normal range? Explain.

    Age (yr) Words
    1.0 3
    1.5 22
    2.0 272
    2.5 446
    3.0 896
    3.5 1222
    4.0 1540
    4.5 1870
    5.0 2072
    6.0 2562
    = 3.30 = 1090.5
         SSx = 23.10 SSy = 7,403,118.48

    SSxy=12,980.50

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