Biology 401 - Biometry

 Fall 2002

Sample Questions for Exam 3 - Answers

Note - there are more questions in this sample than there will be in the real exam

Test significance at alpha = 0.05 unless otherwise indicated.

  1. A regression of weight (in kg) on age (in years) for small children generates b = 2.1 and a = 8.2.  What is the expected weight of a child 4 years 3 months old?
    17.125 kg

  2. Data on the average IQ of children from different sized families are presented in the Excel spreadsheet.  Use a “hand-calculated” regression to determine the relationship between average IQ and the number of children in the family.  Then calculate the 95% confidence interval for the resulting slope and indicate the values below.
    # of children Average IQ
    1 105
    2 102
    3 104
    4 100
    5 97
    6 101
    7 95
    8 93
    9 96
    10 88

    IQ = 106.8 - 1.582 * Number

    95% CI for slope: -2.194 to -0.970
     
  3. In regression, what statistic indicates the amount of the variation in Y that can be explained by X?
    The coefficient of determination, r2

  4. The clutch size for ten individuals of a species of lizard is measured for their first, second and third clutches (data in Excel worksheet). 
      Clutch
    ID 1 2 3
    1 8 10 8
    2 6 8 14
    3 12 12 10
    4 9 10 10
    5 6 7 5
    6 9 9 7
    7 7 10 7
    8 6 10 6
    9 12 12 13
    10 12 12 9

    1. Calculate the Pearson’s correlation coefficient for clutches 1 and 2, and for 1 and 3.
      r1,2 = 0.85     r1,3 = 0.38
    2. Determine if these two correlation coefficients are significantly different.
      Z = 1.585 - less than tcrit of 1.960, therefore not different.
    3. Compare clutches 1 and 2 using a non-parametric method.
      Spearman's correlation gives rs = 0.824 (or thereabouts depending on how you treat the ties - there were more than I intended). This gives P < 0.05.

  5. During a stint working for the MCAT grading service, you are asked to ascertain what degree of association, if any, exists between the verbal, physical and biological scores of students.  What approach would you use to determine this?
    The most appropriate way to do this would be using Kendall's coefficient of concordance.

  6. Shamelessly looking into sealed medical records, you obtain the below data on age and systolic blood pressure in women.  Your goal is to be able to determine the expected blood pressure for a woman based on her age.  Carry out an appropriate analysis of the data, and use your findings to predict the blood pressure of a 60 year old woman.
    ID Age Systolic BP   ID Age Systolic BP   ID Age Systolic BP
    1 42 130 11 64 155 21 71 158
    2 46 115 12 81 160 22 76 158
    3 42 148 13 41 125 23 44 130
    4 71 100 14 61 150 24 55 144
    5 80 156 15 75 165 25 80 162
    6 74 162 16 53 135 26 63 150
    7 70 151 17 77 153 27 82 160
    8 80 156 18 60 146 28 53 140
    9 85 162 19 82 156 29 65 140
    10 72 158 20 55 150 30 48 130

    Using linear regression, BP = 100.4 + .716 * Age. Thus for a 60 year old woman, the predicted BP is 143.
  7. A student survey is undertaken to determine whether Chemistry or Biology has better teachers.  Three professors in each department, each of whom teaches three unique courses, are examined. (The names have been changed to avoid litigation). For each course, a mean score of student satisfaction is taken - data are shown below.  Test the question posed using an appropriate method.
    Chemistry Biology
    Instructor Ratings Instructor Ratings
    Dr. Benzene 3.9, 3.2, 4.1 Dr. Golgi Body 4.2, 4.5, 3.9
    Dr. Enthalpy 4.2, 4.4, 4.0 Dr. Adipose Tissue 4.8, 4.6, 4.4
    Dr. Homonuclear Diatomic Molecule 3.8, 3.6, 4.2 Dr. Displacement Behavoir 4.0, 4.3, 4.1

    Using Nested ANOVA, with instructor nested within department, we get:

    Source SS DF MS F P
    Department 0.642 1 0.642 3.524 0.134
    Instructor 0.729 4 0.182 2.144 0.138
    Error 1.020 12 0.085    

    So no difference among departments in instructor quality.


  8. Recall the question below from a previous practice exam. Analyze the data again, this time using a non-parametric approach.

    You want to determine whether a certain hormone affects growth rates in mammals. Using mice as a model organism, you take two siblings from each of 6 litters of mice, and in each case inject one sibling with the hormone and the other with a placebo. You then weigh the mice two weeks later. The resulting data are below.
    Litter Hormone Placebo
    A 3.6 5.2
    B 3.6 5.5
    C 4.4 4.0
    D 3.7 4.6
    E 4.8 5.3
    F 3.6 3.8

    Using the Wilcoxon paired-sample test, we get T+ = 2 and T- = -19. For n = 6, Tcrit = 0, so no significant effect is seen.

  9. Again, recall the question below from a previous practice exam. Analyze the data again, this time using a non-parametric approach.

    You develop a new nutritional supplement for pregnant women and run an experiment to test its effectiveness.  You convince 10 expectant mothers to try the supplement, and they have babies with the birth weights shown below.  You also know that U.S. birth weights have a median value of 3.4 kg. Does the sample differ significantly from this value?

    Observed birth weights: 2.9, 3.0, 2.7, 3.7, 2.6, 3.2, 3.1, 2.7, 2.8, 3.5 kg

    Using the sign test, we get 8 minuses and 2 pluses, giving P = 0.088.

  10. A study is undertaken to examine the possible benefits of two different vitamin regimens on growth in infants.  Seven sets of triplets are used for the study, with each child of a given family receiving one of the two regimens or no supplement.  Weight gain is then measured over the next two years (data below).  Determine whether either of the vitamin treatments is useful using a non-parametric test.
    Family No supplement Regimen 1 Regimen 2
    A 11.2 9.3 10.4
    B 9.7 12.0 11.5
    C 8.2 9.4 8.9
    D 9.1 10.1 7.9
    E 11.0 10.3 10.8
    F 7.3 9.1 8.4
    G 8.2 8.3 10.1

    Friedman's test gives rank sums of 12, 16 and 14 for the three groups, giving chi-square = 1.143, less than the critical value of 5.991.